Treatment of inorganic electrolytes and organic...

ACPD7, 10971–11047, 2007

Treatment ofinorganic electrolytes

and organiccompounds

S. L. Clegg et al.

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Atmos. Chem. Phys. Discuss., 7, 10971–11047, 2007www.atmos-chem-phys-discuss.net/7/10971/2007/© Author(s) 2007. This work is licensedunder a Creative Commons License.

AtmosphericChemistry

and PhysicsDiscussions

Effects of uncertainties in thethermodynamic properties of aerosolcomponents in an air quality model – PartI: Treatment of inorganic electrolytes andorganic compounds in the condensedphaseS. L. Clegg1, M. J. Kleeman2, R. J. Griffin3, and J. H. Seinfeld4

1School of Environmental Sciences, University of East Anglia, Norwich NR4 7TJ, UK2Department of Civil and Environmental Engineering, University of California, Davis CA95616, USA3Institute for the Study of Earth, Oceans and Space, and Department of Earth Sciences,University of New Hampshire, Durham, NH 03824, USA4Department of Chemical Engineering, California Institute of Technology, Pasadena, CA91125, USA

Received: 1 June 2007 – Accepted: 28 June 2007 – Published: 26 July 2007

Correspondence to: S. L. Clegg ([email protected])

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Abstract

Air quality models that generate the concentrations of semi-volatile and other condens-able organic compounds using an explicit reaction mechanism require estimates ofthe physical and thermodynamic properties of the compounds that affect gas/aerosolpartitioning: vapour pressure (as a subcooled liquid), and activity coefficients in the5

aerosol phase. The model of Griffin, Kleeman and co-workers (e.g., Griffin et al., 1999;Kleeman et al., 1999) assumes that aerosol particles consist of an aqueous phase,containing inorganic electrolytes and soluble organic compounds, and a hydrophobicphase containing mainly primary hydrocarbon material. Thirty eight semi-volatile reac-tion products are grouped into ten surrogate species which partition between the gas10

phase and both phases in the aerosol. Activity coefficients of the organic compoundsare calculated using UNIFAC. In a companion paper (Clegg et al., 2007) we examinethe likely uncertainties in the vapour pressures of the semi-volatile compounds andtheir effects on partitioning over a range of atmospheric relative humidities. In thiswork a simulation for the South Coast Air Basin surrounding Los Angeles, using lower15

vapour pressures of the semi-volatile surrogate compounds consistent with estimateduncertainties in the boiling points on which they are based, yields a doubling of thepredicted 24-h average secondary organic aerosol concentrations. The dependencyof organic compound partitioning on the treatment of inorganic electrolytes in the airquality model, and the performance of this component of the model, are determined20

by analysing the results of a trajectory calculation using an extended version of theAerosol Inorganics Model of Wexler and Clegg (2002). Simplifications are identifiedwhere substantial efficiency gains can be made, principally: the omission of dissoci-ation of the organic acid surrogates; restriction of aerosol organic compounds to oneof the two phases (aqueous or hydrophobic) where equilibrium calculations suggest25

partitioning strongly in either direction; a single calculation of activity coefficients of theorganic compounds for simulations where they are determined by the presence of onecomponent at high concentration in either phase (i.e., water in the aqueous phase, or

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a hydrocarbon surrogate compound P8 in the hydrophobic phase) and are thereforealmost invariant. The implications of the results for the development of aerosol modelsare discussed.

1 Introduction

Atmospheric models of the inorganic components of aerosols, principally ammonium,5

sulphate, sea salt, components of wind blown dust, and nitrate, are relatively well es-tablished (e.g., Zhang et al., 2000; Jacobson, 1997; Nenes et al., 1998; Wexler andClegg, 2002). The models are based upon extensive laboratory data for physical andthermodynamic properties of the relatively small number of components present, equi-librium constants for the formation of solids and gases, and activity coefficient models10

of varying levels of complexity and accuracy which are used to calculate aerosol wateruptake and the activities of solute species needed to estimate gas/aerosol partitioning.

The composition and properties of the organic portion of aerosols, particularly sec-ondary compounds formed from gas phase reactions, are much less well understood(Kanakidou et al., 2005). A significant fraction of the organic aerosol material remains15

uncharacterised, and the thermodynamic properties of the secondary compounds thathave been identified (e.g., Yu et al., 1999; Jaoui et al., 2005) have generally not beenmeasured. Evidence suggests that oligomerisation and other aerosol phase reactionscan be important, and enhance the formation of secondary organic aerosol (SOA) ma-terial (Jang et al., 2003; Kalberer et al., 2006). The most common atmospheric codes20

treat the organic components of aerosols, including SOA formation, using a lumpedtwo component approach developed to represent the results of chamber experiments(Odum et al., 1996; Griffin et al., 1999). For example, in the Community Multiscale AirQuality (CMAQ) model of U.S. EPA, anthropogenic and biogenic SOA-forming materialare each represented by this two component approach and partition into the organic25

fraction of the aerosol which also contains primary organic material (Yu et al., 2007).There are no interactions with the inorganic components of the aerosol. An alternative

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approach is an explicit model in which the formation of condensable and semi-volatileorganic compounds are first calculated using a gas phase kinetic model (e.g., Jenkin etal. 2003; Griffin et al., 2002). The reaction products can then be grouped into a smallernumber of surrogates in order to make gas/aerosol partitioning calculations efficient(e.g., Bian and Bowman, 2005; Griffin et al., 2003). The key thermodynamic properties5

of these compounds or surrogates – particularly their vapour pressures and activitiesin the aerosol liquid phase(s) – can be estimated using structure-based methods. Weevaluate the uncertainties associated with the vapour pressures of the surrogate com-pounds in a second study (Clegg et al., 2007), hereafter referred to as Paper II. Thiswork focuses on some of the key elements of the activity coefficient treatment of both10

inorganic and organic aerosol compounds, and their impact on calculated gas/aerosolpartitioning. A current state-of-the-science air quality model (Kleeman et al., 1997;Kleeman and Cass, 1998; Kleeman et al., 1999) is used in the analysis in order tounderstand the practical effects of errors and uncertainties in atmospheric simulations.

The elements of a generalised scheme for including the organic elements of aerosols15

in air quality and other atmospheric models are shown in Fig. 1, based on that de-scribed by Pun et al. (2002). Primary emissions of particles and condensable organicvapours are represented on the lower left hand side of the figure, and reactions pro-ducing semi-volatile products above. The large number of compounds is reduced to asmaller number of surrogates for the gas/particle partitioning calculation. It is possible20

that multiple organic phases could exist in the aerosol and that each of the surrogatecompounds would be present in all of them. This would create a difficult and time con-suming optimisation problem. The simplest approach is shown in Fig. 1: the aerosolhas an aqueous phase dominated by inorganic ions, and a hydrophobic phase contain-ing the primary compounds which have a mainly hydrocarbon character and which are25

insoluble in water. In the model of Griffin, Kleeman and co-workers, hereafter referredto as the UCD-CACM model (where CACM stands for the Caltech Atmospheric Chem-istry Mechanism), the primary compounds are assigned directly to the hydrophobicaerosol phase in step (a) in the figure.

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In step (b) in Fig. 1 the partitioning of the semi-volatile surrogate compounds be-tween gas and aerosol phases is calculated for one or more aerosol size classes eitherdynamically, or assuming thermodynamic equilibrium. This process is driven by the(subcooled) liquid vapour pressures of the surrogate compounds and the associatedenthalpies of vaporisation, and the activities in the aqueous and hydrophobic phases.5

These activities, and the amounts of liquid water (mainly controlled by inorganic ions)and hydrophobic compounds present, determine their partitioning between the two liq-uid phases (step c). The amounts of some compounds can be enhanced in the aque-ous phase by step (d), dissociation, which is determined from the dissociation con-stants and the activities of the undissociated organic molecule, H+

(aq) and the organic10

anions. Condensed phase oligomerisation and other reactions, which are representedby step (e), may form larger molecules of low volatility, effectively sequestering someof the semi-volatile surrogates in the aerosol until wet or dry deposition removes themfrom the atmosphere. There is evidence that high molecular weight hydrocarbons andother primary emissions are able to partition between gas and aerosol phases (Fraser15

et al., 1997, 1998), step (f), which is included here for completeness.The treatment illustrated in Fig. 1 is conceptually simple, but still requires more in-

formation than is currently available to quantify properties and define each step of thegas/aerosol partitioning process accurately. The UCD-CACM model corresponds tothe schematic but with the omission of steps (e) and (f). In this study and in Paper20

II we examine uncertainties in predictive methods that affect gas/aerosol partitioningof semi-volatile compounds (the net effect of steps (b), (c) and (d) in Fig. 1). Thiswork focuses on the calculation of activity coefficients, the effects of the inorganic ther-modynamic treatment on the partitioning of semi-volatile compounds, the selection ofsurrogate compounds and the assignment and estimation of their properties.25

In order to relate these studies to their practical effects in air quality calculations, weuse the 2-D Lagrangian version of the UCD-CACM air quality model as an example.We include model simulations of a series of 24 air parcel trajectories ending at twolocations in Southern California on successive hours of the day on 9 September 1993.

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The main location studied was Claremont, California, which was heavily influenced byanthropogenic emissions from urban Los Angeles during that period. Output from theUCD-CACM model for gas/aerosol partitioning and total amounts of each species perm3 were used as input to a flexible code (Clegg, 2004) incorporating the AIM modelof Wexler and Clegg (2002), and able to calculate the state of systems corresponding5

to the schematic in Fig. 1 (excluding the reactions in step e). In this work we referto this extended model simply as AIM. Gas/aerosol partitioning in the UCD-CACMmodel is calculated dynamically, whereas AIM determines the equilibrium state of anaerosol system. In addition, the two models treat the thermodynamic properties of theinorganic component of the aerosol very differently. We therefore compare the results10

of the two models in some detail, for both inorganic and organic components, in orderto fully understand these differences and their effects in air quality simulations. Notethat the UCD-CACM model and AIM results are compared for situations where theUCD-CACM result is close to equilibrium, or with equilibrium properties such as activitycoefficients and partial pressures calculated directly using the UCD-CACM model. This15

ensures consistency. The results are relevant, first, to the general development ofatmospheric aerosol models based upon an explicit chemistry and corresponding toFig. 1, highlighting particular areas in which a better quantitative understanding of thephysical chemistry is needed. Second, they identify elements of the UCD-CACM modelon which future work is likely to focus.20

In the section below we describe the main features of the thermodynamic modelsused and the chemical system treated, and summarise the calculation of solvent andsolute activities and key uncertainties.

2 The models

The UCD-CACM source-oriented air quality trajectory model is a reactive photochem-25

ical transport model that describes pollutant emissions, transport, chemical transfor-mation, and deposition (Kleeman et al., 1997; Kleeman and Cass, 1998; Kleeman et

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al., 1999). The model includes all of the atmospheric operators used in the full 3-D UCD/CIT airshed model (Kleeman and Cass, 2001; Held et al., 2004; Ying et al.,2007) but the Lagrangian trajectory framework is more computationally efficient thanthe Eulerian approach. Particles emitted from different sources are tracked separatelythrough the full atmospheric simulation to capture the heterogeneous nature of real5

atmospheric particulate matter. Gas-phase precursors can also be tracked throughthe photochemical mechanism to identify source-contributions to secondary reactionproducts (Mysliwiec and Kleeman, 2002; Ying and Kleeman, 2007; Kleeman et al.,2007). The trajectory framework is not capable of representing vertical wind shear orhorizontal turbulent diffusion.10

The Caltech Atmospheric Chemistry Mechanism (CACM) is used to describe thephotochemical reactions in the atmosphere including the formation of semi-volatileproducts leading to the production of secondary organic aerosol. The modelled sys-tem consists of 139 gas-phase species participating in 349 chemical reactions, andinorganic ions, gases, and solids (Griffin et al., 2002). For the purpose of calculating15

gas/aerosol partitioning, the semi-volatile species generated by chemical reaction, andcapable of forming SOA, are combined into a set of 10 surrogate species A1-5 and B1-5 (Griffin et al., 2005). There are, in addition, 8 primary organic hydrocarbons (P1-8)which are assumed to exist only in the aerosol phase.

Aerosol particles in the UCD-CACM model can consist of 2 liquid phases (see Fig. 1):20

first, an aqueous phase containing water, inorganic ions, and some fraction of the SOAsurrogates and their dissociation products; second, a hydrophobic phase containingthe primary hydrocarbons and the SOA surrogates (non-dissociated molecules only)which equilibrate between the two phases. Inorganic solids are able to form, basedupon their known deliquescence relative humidities and equilibrium constants. No or-25

ganic solids form, even at low relative humidity (RH), and the hydrophobic aerosolphase is assumed always to exist as a subcooled liquid. This assumption is justifiedby the fact that the very large numbers of organic compounds likely to be present inreal atmospheric aerosols will greatly depress the temperature at which solids will form

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(e.g., Marcolli et al., 2004).Aerosols are represented by 15 size bins, with compositions determined by the orig-

inal source and the dynamically driven partitioning of water, NH3, HNO3, HCl and othertrace gases, and chemical reactions occurring in both the aerosol and gas phases(Kleeman et al., 1997; Kleeman et al., 2007). Bins 1 to 5, corresponding to particles5

with aerodynamic diameter smaller than 0.1µm, are not considered in the comparisonshere, in part because the focus of this study is on effects on the total amounts of or-ganic compounds in the aerosol phase – most of which occurs for particles larger than0.1µm, and also because the reference AIM model (Clegg, 2004; Wexler and Clegg,2002) does not include the Kelvin effect which has an important effect on partitioning10

for particles below this size.The AIM model calculates the thermodynamic equilibrium state of gas/aerosol sys-

tems containing known total amounts of material per m3 (Wexler and Clegg, 2002). Asingle bulk aerosol phase is assumed. The models have recently been extended toinclude organic compounds with user-specified properties, ammonia and water disso-15

ciation, and a hydrophobic liquid aerosol phase (Clegg, 2004). Organic compounds areable to partition between the gas phase and both fractions of the aerosol or, if required,their occurrence and partitioning can be limited to phases chosen by the user. Themodel is thus able to emulate the thermodynamic treatment of gas/aerosol partitioningin atmospheric codes of a range of complexity, including both the UCD-CACM model20

and, for example, the treatment of SOA formation in CMAQ (Yu et al., 2007).The gas/aerosol partitioning of water-soluble organic semi-volatile compounds links

to the thermodynamics of the inorganic portion of the aerosol mainly via the amountof aerosol water, dissociation to H+

(aq) and organic anions, and interactions betweeninorganic ions and uncharged organic molecules that lead to changes in the activity25

coefficients. Variations between models will be most apparent at low relative humidityboth because differences between calculated water activity/concentration relationshipsof the solutes tend to be greatest at low RH, and especially because models maynot predict the same amounts of inorganic solids to form causing large differences in

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predicted aerosol water content. The treatment of the activity coefficients of H+(aq), and

organic anions can also differ, thus affecting the calculated degrees of dissociation ofthe organic compounds.

The chemical components of the atmospheric system, and the main elements ofboth models that affect calculated gas aerosol partitioning, are described below.5

2.1 Chemical system

The inorganic ions in the aerosol system are H+, NH+4 , Na+, SO2−

4 , NO−3 and

Cl−. The gases NH3, HNO3 and HCl are also included, as are the solids(NH4)2SO4(s), (NH4)3H(SO4)2(s) (letovicite), NH4HSO4(s), NH4NO3(s) and NaCl(s). Allthese species are included in both models. Further solids 2NH4NO3.(NH4)2SO4(s),10

3NH4NO3.(NH4)2SO4(s), and NH4HSO4.NH4NO3(s) are treated by the AIM model only.The 8 primary hydrocarbons (P1-8) and 10 semi-volatile surrogate species (A1-5, andB1-5), which are included in both models, are described in Appendix A.

The semi-volatile species present in the aerosols are assumed to partition at equi-librium between the two liquid phases at all times, according to:15

xi (aq)fi (aq) = xi (org) fi (org) (1)

where subscript (aq) indicates the mole fraction (x) or mole fraction activity coefficient(f ) of each species i in the aqueous phase, and subscript (org) the same quantitiesin the hydrophobic liquid phase. The activity coefficient f is relative to a pure liquidreference state (i.e., fi=1.0 when xi=1.0). The equilibrium partial pressures (pi ) of the20

semi-volatile organic surrogates over the liquid aerosol, which drive their mass transferbetween vapour and aerosol phases, are calculated according to:

pi = xi fipoi (2)

where poi is the subcooled liquid vapour pressure of component i , and xi is the mole

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fraction of organic compound i in the aqueous and/or hydrophobic phases. The disso-ciation of the organic acids and diacids H2X is governed by the following equations:

Kd1 = mH+γH+mHX−γHX−/(mH2X γH2X) (3a)

Kd2 = mH+γH+mHX2−γX2−/(mHX−γHX−) (3b)

where Kd1 (mol kg−1) and Kd2 (mol kg−1) are the first and second stepwise dissociation5

constants, respectively, prefix m denotes molality, and γi is the molality based activ-ity coefficient of the indicated species. (See Robinson and Stokes, 1965, for relation-ships between activity coefficients on the different concentration scales.) The treatmentof singly dissociating acid HY is analogous to that above but based on the equationKd = mH+γH+mY−γY−/(mHY γHY). The dissociating organic surrogate species are10

B1, B2, A1, A2 and A4, and their dissociation constants are listed in Appendix A. Thecalculation of the activity coefficients used in Eqs. (3a, b) by both models is discussedin the section below.

The UCD-CACM model calculates the formation of inorganic solids by minimisingthe Gibbs free energy of the inorganic species. Thermodynamic information for the15

minimization calculation is provided by Wexler and Seinfeld (1991). In the AIM model,the equilibrium constants listed in Table 2 of Clegg et al. (1998a) are used to obtainGibbs energies of formation of the solids and gas phase species, and no independentknowledge of the deliquescence relative humidities of the individual solid phases isrequired. The Henry’s law constants of the gases HNO3, NH3, and HCl that govern the20

equilibrium of these species between aqueous and gas phases are well established(e.g., Carslaw et al., 1995; Clegg et al., 1998a, b), and the effects of any differences inthe values of these constants used in the two models are likely to be small.

In the UCD-CACM model each aerosol size bin exchanges water dynamically withthe surrounding gas-phase (equilibrium is not assumed). The effective water activity25

above each particle surface is calculated according to the method described by Prup-pacher and Klett (1978) to account for modification of the surface temperature duringrapid condensation or evaporation of water vapour. Thus the larger aerosol size bins

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and gas phase may not always be close to equilibrium with respect to water. The watercontent of each size bin is also not permitted to become zero, and a residual amountis always present. This is set according to the amounts of inorganic species in theaerosol.

In the extended AIM model described by Clegg (2004) the Gibbs energies of for-5

mation of the additional aqueous species NH3 and OH− are obtained, as a function oftemperature, from the equilibrium constants for dissociation of water and of ammonium,and the Gibbs energies of formation of H2O, H+, and NH+

4 , using Eq. (11) of Wexlerand Clegg (2002). The molality based dissociation constants of the surrogate organicspecies, their Henry’s law constants or sub-cooled liquid vapour pressures po

i and as-10

sociated enthalpy changes are entered as input data to the program. Where poi is used,

the logarithm of the infinite dilution activity coefficient in water (f∞i ) and its slope withrespect to temperature are also entered. These quantities are used internally within theprogram to calculate the Gibbs energies of formation used by the equilibrium solver.Activity coefficients determined using UNIFAC for the uncharged organic molecules in15

both liquid phases are converted to a reference state of infinite dilution with respect towater for use in Eq. (23) of Wexler and Clegg (2002). Values for the aqueous phaseare adjusted, as are those of the ions and water, to take account of the alteration of thedefinition of the mole fractions in the solution to include all the species present, ratherthan just ions + water, or organics + water. The approach taken is described by Clegg20

et al. (2001). Primary surrogate compounds are constrained, in most calculations, tothe hydrophobic phase. The dissociation of surrogates B1, B2, A1, A2 and A4 in theaqueous phase, to produce additional H+ and organic anions, occurs only in the aque-ous phase. The equilibrium state of each test system is determined by minimizationof Eq. (23) of Wexler and Clegg (2002), with additional terms to account for the extra25

liquid phase.

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2.2 Solvent and Solute Activities

In the UCD-CACM model the mean molal activity coefficients of the inorganic elec-trolytes present are calculated using the method of Kusik and Meissner (1978) as im-plemented by Wexler and Seinfeld (1991). The method is based upon the propertiesof the single electrolytes present, which are correlated with single parameter equations5

using data for 25◦C. The inorganic composition of the aerosol must be specified interms of electrolyte molalities, rather than those of the aqueous ions, in order to cal-culate activity coefficients using the Kusik and Meissner method. These are obtainedby assigning anions to cations in proportion to the cation charge mizi for cation i di-vided by the total charge of all cations (Σimizi ), and the corresponding assignment of10

cations to anions. For the group of ions Na+, NH+4 , H+, Cl−, NO−

3 , and SO2−4 there are

9 possible electrolytes. This approach is the same as originally proposed by Reilly andWood (1969), and also used by Clegg and Simonson (2001) in an activity coefficientmodel in which electrolytes rather than ions are treated as the basic components. Theuse of a very simple correlating equation for the thermodynamic properties of single15

solute solutions in the Kusik and Meissner method, the lack of treatment of mixture ortemperature effects, and the lack of explicit recognition of the key HSO−

4(aq) ↔ H+(aq) +

SO2−4(aq) equilibrium, make the method less accurate than the more complex, but com-

putationally intensive, approaches used in AIM and in other atmospheric codes (e.g.,Zhang et al., 2000; Nenes et al., 1998; Jacobson, 1997).20

In the UCD-CACM model, osmotic coefficients of aqueous electrolytes from Tanget al. (1995) are used to calculate the equilibrium water activities and vapour pres-sures of each aerosol size bin using the Zdanovskii-Stokes-Robinson (ZSR) relation-ship (Stokes and Robinson, 1966; Seinfeld and Pandis, 2006). The water associatedwith the organic compounds in the aqueous phase is calculated using UNIFAC (Fre-25

denslund, 1975). As noted above, water exchange between the aerosol and the gasphase is controlled dynamically and is also subject to two limits: the aerosol water con-tent of each size bin is not allowed to fall below a minimum value which is related to the

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amounts of inorganic solutes present, nor is the ionic strength permitted to rise above100 mol kg−1.

In the extended AIM model both solute and solvent activity coefficients are estimatedfor mixed inorganic/organic aqueous solutions by the method described by Clegg etal. (2001). The Pitzer-Simonson-Clegg (PSC) equations (Clegg et al., 1992) are used5

for the inorganic component of the solution and UNIFAC for the uncharged organicspecies in the aqueous phase of the aerosol, and for all components in the hydropho-bic phase. Both mixture effects (between inorganic ions) and the variation of activitycoefficients with temperature are taken into account in the PSC model, which yieldsvalues of single ion activity coefficients. The sulphate/bisulphate equilibrium is also10

treated explicitly, with HSO−4(aq) as a separate ionic species (Clegg and Brimblecombe,

1995). Aerosol water content is calculated as a part of the minimisation of the totalGibbs energy of the system that is used to calculate its equilibrium state at fixed T andRH, and can be zero (corresponding to an aerosol containing only inorganic solids).

The UCD-CACM inorganic aerosol model includes inorganic ions Na+, NH+4 , H+, Cl−,15

NO−3 , and SO2−

4 , although the treatment of these species is somewhat approximate(see previous discussion). The inorganic model used in the AIM calculations is that forH+ – NH+

4 – SO2−4 – NO3 – H2O (AIM Model II on the web site http://www.uea.ac.uk/

∼e770/aim.html). This has been modified for use in this study in two ways. First, theequilibria H2O(l) ↔ H+

(aq) + OH−(aq), and NH+

4(aq) ↔ NH3(aq) + H+(aq), have been added so20

that OH− and NH3 are additional aqueous phase species. No interaction parametersfor these species in the PSC model have yet been determined. The activity coefficientsare calculated using Eqs. (17), (26) and (31) for OH− (which includes the Debye-Huckellimiting law), and Eq. (15) for NH3, from Clegg et al. (1992). The aerosols simulatedin this study also contain Na+ and Cl−. We have therefore included parameters for25

Na+ interactions with SO2−4 , HSO−

4 , NO−3 and Cl− at 25◦C from AIM model III (Clegg et

al., 1998b), for Cl− with H+ as a function of temperature from Model I (Carslaw et al.,1995), and for interactions of Cl− with Na+ and NH+

4 from Model III. Ternary (mixture)interaction parameters were also taken from Model III, where available. The variation

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of the Henry’s law constant of HCl with temperature is taken from Model I. Organicacid anions from the dissociation of surrogates were incorporated into the model byassuming that the parameters for their interactions with cations are the same as thosefor SO2−

4 (doubly charged anions) or HSO−4 (singly charged anions).

The UNIFAC group interaction parameters used by both models in this study are5

those listed in the Supplementary Material to Hansen et al. (1991), and do not includelater additions. UNIFAC group definitions for each organic surrogate molecule in theUCD-CACM model are listed in Appendix A. We note that the structures –O–NO2 can-not be defined in terms of the currently available groups, and substitutions have beenmade for this study. Also, parameters for some interactions are unknown. The effects of10

these uncertainties have not been quantified. The partitioning of SOA surrogate com-pounds A1-5 and B1-5 between the aqueous and hydrophobic phases in the aerosolis driven by the activity coefficients, estimated using UNIFAC, for the two systems A1-5and B1-5 plus water (aqueous phase) and A1-5 and B1-5 plus P1-8 (hydrophobic or-ganic phase). The governing equation is simply Eq. (1) for the mole fraction and activity15

coefficient of each component i in the two phases.The UNIFAC equations are based upon functional groups, and smaller structural

units, as the fundamental entities in solution from which all molecules present aremade up. Consequently, the assignment of individual semi-volatile compounds to thesurrogates used in the UCD-CACM or other models – where these surrogates are20

based upon structural similarities – is likely to produce results that are consistent withthose that would be obtained for the individual compounds. We have tested this bycalculating liquid/liquid partitioning for a system containing 1 mole of water, 1 moleof P8 (the dominant hydrophobic compound in the trajectory calculations discussedfurther below), and 0.01 moles of each of the thirty eight compounds making up the25

ten surrogates A1-5 and B1-5. The results, see Fig. 2, show broad agreement: thecomponents of A1-5 occur mainly in the aqueous phase, and most of the componentsof B3 to B5 occur in the hydrophobic phase, which is consistent with the calculatedpartitioning of the surrogates. Agreement is poorer for B2, and the components of

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B1 appear to have a mainly hydrophobic nature whereas B1 itself is predicted to bewater soluble. This is likely to be due to the chosen locations of the functional groupson the surrogate molecules, which contain similar groups and have similar molecularformulae to the molecules they represent. We note that in aerosols at moderate to highRH the amount of liquid water is likely to greatly exceed the amount of hydrophobic5

material present; consequently in the trajectory calculations discussed further below asignificant fraction of total aerosol B2 can be found in the aqueous phase despite thesmall aqueous fraction shown in Fig. 2.

Our original intent when planning this study was to focus on salt/organic interac-tions in the aqueous phase, usually referred to as “salting in” or “salting out”, which10

is an element of the activity coefficient modelling of the aqueous phase that affectssteps (b) (c) and (d) in Fig. 1. This behaviour has been studied in measurements ofdeliquescence relative humidity (DRH) and solubility in mixtures of dicarboxylic acidsand salts (e.g., Marcolli et al., 2004; Salcedo, 2006; Clegg and Seinfeld, 2006a,b andreferences therein). The effect on DRH is already predicted, at least approximately,15

by current methods of estimating aerosol water content (Clegg and Seinfeld, 2006a),and the salt effect on the activity coefficients of organic solutes is probably smallerin magnitude than uncertainties related to vapour pressures, the choice of surrogatespecies and the choice of activity coefficient model. Furthermore, it is difficult to includesuch interactions in models in a reliable and robust way to very high (supersaturated)20

concentrations. Salt/organic interactions have therefore been omitted here.In the absence of activity coefficient model parameters for interactions between ions

and undissociated organic molecules, noted above, the extended AIM model yieldsmolality based activity coefficients for both types of species that are unaffected by thepresence of the other (see Eqs. 1a and b of Clegg et al., 2001). The approach in the25

UCD-CACM model, described by Pun et al. (2002), is found to be equivalent whenthe definitions of mole fractions and mole fraction activity coefficients used in the com-puter code are taken into account. However, there are some differences between thetwo models. First, organic and inorganic activity coefficient calculations in the UCD-

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CACM model are not fully coupled with respect to pH. Inorganic liquid/solid equilibriaare solved first, followed by those involving the organic compounds: uptake of water,the dissociation of the acid surrogate species and partitioning between the two aerosolphases. The H+ ion concentration in the aqueous phase is modified (increased) bythe dissociation of the organic acids, but this change is not fed back into the inor-5

ganic calculation. In most situations the amounts of water-soluble dissociating organiccompounds in the aerosol are small relative to the inorganic content, so the effect ofthis simplification is likely to be negligible. (A possible exception is where the aerosol isclose to neutral pH, in which case the organic compounds could be a significant sourceof H+ and so influence equilibria with gas phase NH3, HNO3 and HCl.)10

Second, in the UCD-CACM model the values of the activity coefficients of the organicacid molecules and anions in Eq. (3), required to calculate dissociation, are both as-sumed to be equal to the value obtained using UNIFAC for the undissociated molecule.This is equivalent to assuming values of unity, since the activity coefficients in the equa-tions cancel. The value of γH+ is also assumed to be unity. We note that Pun et al.15

(2002) assumed unit values for only the activity coefficients of H+ and the organic an-ions in Eq. (3). The effect of the treatment of activity coefficients in the UCD-CACMmodel is to lower the dissociation of organic acids, and this is discussed further below.The effect will vary with both aerosol composition and concentration.

2.3 Vapour pressures20

In the UCD-CACM model, subcooled vapour pressures of secondary organic surro-gates A1-5 and B1-5 are estimated by the method of Myrdal and Yalkowsky (1997).This uses the boiling temperature at atmospheric pressure (Tb), the entropy of boil-

ing (∆Sb), and the heat capacity change upon boiling (∆C(gl )p ). The normal boiling

points used in previous applications of the UCD-CACM model were obtained either25

from measurements or using the estimation software of Advanced Chemistry Devel-opments (ACD) which is described in a manuscript by Kolovanov and Petrauskas (un-

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dated), (B. L. Hemming, personal communication). Full details, and a comparison withother boiling point and vapour pressure prediction methods, are given in Paper II (Clegget al., 2007).

2.4 Key uncertainties

Within the scheme shown in Fig. 1 – omitting both gas phase reaction mechanisms and5

step (e) from consideration – the main uncertainties affecting gas/aerosol partitioningare associated with the vapour pressures of the semi-volatile compounds, the approxi-mations inherent in the use of surrogate compounds, and calculations of aerosol watercontent and activities in the liquid aerosol. First, realistic predictions of gas/aerosol par-titioning of the semi-volatile organic compounds require accurate estimates of po, and10

the associated enthalpy of vaporisation ∆Hovap of the compounds or their surrogates.

The available methods for vapour pressure prediction, which are based upon the struc-ture and functional group composition, are least accurate for compounds containingpolar groups, and yield widely varying results (see Paper II, Clegg et al., 2007).

Second, the choice of surrogate species, and their structures and functional group15

compositions, are also important. Table 1 of Paper II lists vapour pressures for butaneand related C4 alcohols and carboxylic acids. The addition of first one, and then twopolar functional groups to the butane molecule results in a lowering of po by orders ofmagnitude. The positions of the groups on the molecule also make a large differenceto the vapour pressure, by more than an order of magnitude in some of the examples20

shown in the table. Consequently, if the properties of the surrogate species are aver-ages of the estimated values of the compounds they represent, then the range is likelyto be large.

Third, it is known that UNIFAC, which is used in both models in this study to calcu-late liquid phase activities of the organic compounds in the aerosol, is least accurate25

for molecules containing polar functional groups. In addition, assumptions about theactivity coefficients of organic anions in Eqs. (3a, b) need to be made in order to calcu-late dissociation. It is also worth noting that both models used here to calculate activity

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coefficients ignore interactions that may occur between the two inorganic and organic(uncharged) species, partly due to a lack of data and partly because of the lack ofa satisfactory way of representing them over very wide ranges of concentration. Weexamine the effects of these uncertainties below.

3 Comparisons5

3.1 Atmospheric simulations (base case)

Here we focus mainly on a single diurnal cycle from time 00:00 to 24:00 PST on 8September 1993, for the trajectory shown in Fig. 3. Over this period the air parceltravels from over the Pacific Ocean to central Los Angeles and then to Claremont. Bothtotal (gas + aerosol) and aerosol amounts of SO2−

4 , NH+4 , NO−

3 and Na+, from level 110

of the UCD-CACM model simulation (from zero to 38 m above ground), are shown inFig. 4. The amounts of SO2−

4 , Na+, and also NH+4 in the aerosol (because H+ is only

present in a small amount, and because of the overall requirement of electroneutrality)are essentially fixed. There is a small addition of sea salt to the aerosol as the parcelreaches the coast at 13:00 PST, and large addition of ammonia as the parcel passes15

over the Chino dairy region at 18:00 PST and reaches Claremont the next day. Figure 5shows the total concentrations of the 10 semi-volatile surrogate species over the diurnalcycle. Of the surrogates A1-5, A5 dominates in the early morning, A2 during the middleof the day, and both A2 and A5 in the evening. The B surrogate species present in thehighest total concentrations are B2-4, and the amounts increase over the course of20

the diurnal cycle as the air parcel encounters anthropogenic emissions. Surrogate P8constitutes well over 90 mol% of the involatile primary organic compounds present inthe system and occurs at highest concentration late in the day.

Values of T and RH are shown in Fig. 6 for the diurnal cycle. Relative humidityranges from about 40%, for which the acid sulphate aerosols would be expected to25

contain very little water or exist as dry crystals, to 80% which is the deliquescence RH

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of ammonium sulphate over the relatively narrow range of temperature (289 to 301 K)experienced in this cycle. At this higher RH the acid sulphate aerosol particles are fullyliquid.

In the next section, the aggregate aerosol composition (the sum of the contentsof bins 6 to 15) and the range of composition across the particle size spectrum are5

examined and model results compared. The effects of differences in the inorganicelements of the thermodynamic models on aerosol composition and partitioning ofNH3, HNO3 and the semi-volatile organic compounds are also discussed.

3.1.1 Inorganic component behaviour

In the first set of model comparisons, the total amounts of all species in each of the 1010

aerosol size bins were fixed to the values calculated by the UCD-CACM model. Theequilibrium properties of the aerosol in each size bin, including partitioning between theaqueous and hydrophobic phases and the formation of solids, were then recalculatedusing AIM.

The total amounts of aerosol water, the sum of the values in bins 6 to 15, calculated15

by both models over the diurnal cycle are shown in Fig. 7a. For RH above about 60%(from midnight to 8 or 9 am) the totals agree closely. For the whole of the cycle theamounts of organic surrogate compounds in the aerosol are small, as is nitrate, and thesmall differences in total water for high RH reflect differences in the representation ofthe thermodynamic properties of acid ammonium sulphate by the two models and the20

fact that partitioning of water is calculated dynamically in the UCD-CACM model andequilibrium is not assumed. After 09:00 a.m., as RH falls, the AIM reference modelpredicts consistently less water in the aerosol which dries out (all size bins) betweenabout 11:00 a.m. and 01:00 p.m. During this period the water contents of all the aerosolbins in the UCD-CACM model reach their lower permitted limits. The solids predicted25

by the AIM model are shown in Fig. 7b. From 01:00 a.m. to 08:00 a.m., for whichthe predicted total water amounts of the two models agree closely, the only solid thatoccurs is (NH4)2SO4(s). The smaller amounts of water predicted by AIM at midnight,

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and the drying out of the aerosol between 09:00 a.m. and 01:00 p.m., are associatedwith the formation of letovicite. After 02:00 p.m. AIM again predicts less aerosol waterthan does the UCD-CACM model. This difference is associated both with the lowerlimit of aerosol water being reached in the UCD-CACM model, and with the formationof double salt 2NH4NO3.(NH4)2SO4(s) in addition to (NH4)2SO4(s) being predicted by5

AIM. The double salt is not included in the UCD-CACM model.We further compared the inorganic thermodynamic elements of the two models by

examining the calculated equilibrium properties of the aerosol across all the size binsat 08:00 a.m. (T = 289.6 K, RH = 0.8098), for which both models predict all particlesize bins to be fully liquid. The aerosol water contents predicted by both models are10

shown in Fig. 8 for all size bins and agree well. Over 80% of the total water massresides in bins 6 to 10. The inorganic composition of the aerosol, Fig. 9, varies fromapproximately NH4HSO4 (i.e., 1:1 (NH4)2SO4:H2SO4) for bins 6 and 7 to slightly acidi-fied ammonium sulphate at the largest sizes. The small amount of NO−

3 present peaksin bins 8 to 12, but is present in greatest proportion in the higher numbered bins. We15

note that 3.3×10−9 mol m−3 of the non-volatile primary organics, mainly P8, are presentin the hydrophobic phase, and a total of 2.0×10−11 moles of SOA surrogates A1-5 andB1-5 are distributed between the two liquid phases. These amounts are very smallcompared to the inorganic content of the aerosol.

How do the models vary in their prediction of equilibrium partial pressures of HNO320

and NH3 across the size bins, and how do these compare with the actual amounts ofNH3 and HNO3 in the gas phase (which will be different if the two phases are not at ther-modynamic equilibrium)? Figure 10 shows the relative compositions of the size bins,and the ratios of the equilibrium partial pressures of HNO3 and NH3 calculated by AIMto both the UCD-CACM model results and the calculated equilibrium partial pressures25

of HNO3 and NH3 used by the UCD-CACM model to drive inter-phase transport. In theUCD-CACM simulation all size bins are at equilibrium with HNO3(g) (2.33×10−9 atm) asindicated by the overlap of the HNO3 curves in Fig. 10. However, none of the aerosolbins, except 10, are at equilibrium with NH3(g), which is present at a pressure of only

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5.51×10−12 atm.The partial pressures calculated using the two models agree most closely for bin 6

which has a composition (NH4)0.76H1.24SO4 plus trace HNO3. Here pHNO3 (AIM) isabout 1/2 of the value predicted by the UCD-CACM thermodynamic code, and pNH3(AIM) is about 1.5× the UCD-CACM value. In the larger size bins, as composition tends5

more towards (NH4)2SO4, the differences between the equilibrium partial pressurespredicted by the two models increase: pHNO3 (AIM) is lower by almost a factor of 10and pNH3 (AIM) greater by a factor of 20. The reasons for this are investigated inAppendix B, by comparing predictions of both models to data yielding the reciprocal(γNH+

4 /γH+) in aqueous ammonium sulphate solutions. Results suggest that γH+, and10

the activity mH+×γH+, are not predicted well by the Kusik and Meissner (1978) methodused for inorganic thermodynamic properties in the UCD-CACM model. The limitationsof the approach – notably the use of single parameter equations to correlate the activitycoefficients of aqueous electrolytes (Wexler and Seinfeld, 1991) and especially theinability to treat inorganic acid-base equilibria – suggest that these inaccuracies persist15

over a wide range of aerosol composition.Having identified these differences between the thermodynamic models, it is also

important to understand their practical impact, if any, in atmospheric simulations. Ingeneral, the effect of the inaccuracies on calculated NH3 and HNO3 partitioning will begreatest in situations where their distribution between the aerosol and gas phases is20

relatively evenly balanced. For example, consider a case in which 99% of HNO3 in anair parcel is present in the gas phase, and the aerosol and gas phases are approxi-mately at equilibrium. Even order of magnitude changes in the calculated equilibriumpHNO3 above the aerosol would only result in either a reduction of gas phase HNO3 bya few percent of the total, or an increase to a value greater than 99%. The effects of the25

thermodynamic differences in the atmospheric simulation carried out here are small, aswill be shown in comparisons of calculated HNO3 and NH3 partitioning further below.

Next we compare the results of full gas/aerosol partitioning calculations using AIMwith the output of the UCD-CACM model for the complete diurnal cycle. Note that the

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AIM model was only used to recalculate the equilibrium state of the system predictedby the UCD-CACM model (i.e., the total gas plus aerosol phase inorganic and organicspecies amounts per m3 of atmosphere). The purpose of this, for the inorganic com-ponents, is to examine both the effects of differences between the models on solidsformation and, in particular, on gas/aerosol partitioning of HNO3 and NH3.5

In the AIM calculations the system is assumed to consist of a gas phase and asingle bulk aerosol with the aqueous and hydrophobic portions in equilibrium with eachother, with any solids formed, and with the gas phase. The system contains the sametotal amounts of each species per m3 at each time point as in the UCD-CACM model,i.e. the amounts of each species in the gas phase plus the aggregates of bins 6–15.10

As noted earlier, this simplification is necessary because AIM is not currently capableof representing multiple size fractions with different chemical compositions. The effectof bulking the particulate phase for the AIM calculations may somewhat moderate theeffects of differences noted above for HNO3 and NH3, because most of the aerosolmass resides in the bins containing the smaller aerosols, whereas the differences in15

predicted partial pressures are greatest for the less acid aerosols in the larger sizerange.

Total particulate water is shown in Fig. 11, and the total amounts of solids predictedby AIM in Fig. 12. Calculations with AIM were carried out for two cases: (i) all potentialsolids were allowed to form and, (ii) only (NH4)2SO4(s) was able to form. The results,20

in the first case, are similar to those obtained for the calculation using the contentsof the individual size bins, and shown earlier in Fig. 7. However, in this calculationfor the aggregate composition the double salt does not form. The results for case (ii)more closely match the water-limited prediction of the UCD-CACM model (for whichthe aerosol does not dry out), and this case is used in some other comparisons below.25

Amounts of gas phase HNO3 and NH3 predicted by the models are compared inFig. 13. There are two separate factors that can lead to differences: the two activitycoefficient models resulting in different predictions of pHNO3 and pNH3, and disequi-librium between the two phases (in the UCD-CACM model calculations) caused by

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dynamic factors. The results shown in Fig. 10 for 08:00 a.m. indicate equilibrium forHNO3 (which has the higher vapour pressure), but that the amount of NH3 in the vapourphase differs from the equilibrium value by up to a factor of about 3. These are typicalof much of the diurnal cycle. Predicted equilibrium pNH3 from the UCD-CACM modelare shown in Fig. 13 (as vertical bars) to assess this effect.5

Despite the activity coefficient model differences, the amounts of gas phase HNO3predicted by the two models agree well over the whole cycle, and those for NH3 for theperiod after 02:00 p.m. for which pNH3 is greater than about 1×10−8 atm. It is only forthe more acidic system in the early part of the cycle, for which pNH3 is below 10−10 atm,that there are significant differences between the models. There are two reasons for10

this: first, in the morning period, before the large increase in total ammonia in thesystem, the aerosol is acidic and AIM calculations show that about 30% to 65% of totaldissolved SO2−

4 in the aerosol exists as HSO−4 . The equilibrium HSO−

4(aq) ↔ H+(aq) +

SO2−4(aq), which is not treated in the UCD-CACM model, is therefore a major influence

on H+(aq) concentration and activity in this part of the diurnal cycle. The second reason is15

the relative amounts of total gas and aqueous phase ammonia: at 08:00 a.m. the molesof NH3 in the gas phase are just 1% of the total ammonia (NH3(aq) + NH+

4(aq)) in theaerosol. Consequently differences in the equilibrium pNH3 calculated by the activitycoefficient models will be reflected in the amounts of NH3 present in the gas phase.However, these amounts are so small before 02:00 p.m. in the diurnal cycle – below20

about 10−10 atm predicted by both models – that the differences are not significant.In contrast, during the late afternoon the total ammonia in the aerosol liquid phase

(calculated using AIM) is only 1/6 of the amount of gas phase NH3, and a significantamount of ammonia is also present as (NH4)2SO4(s). The aerosol is also much less

acidic, with the amount of HSO−4(aq) negligible compared to SO2−

4(aq). Under these condi-25

tions the differences between the equilibrium partial pressures of NH3 over the aerosolcalculated by the two models are much smaller, and have only a minor effect on theamount of gaseous NH3.

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3.1.2 Organic component behaviour

Using AIM, we have recalculated the liquid/liquid equilibrium of the ten SOA surro-gate species and their equilibrium partial pressures for the aerosol compositions ineach size bin (the sums of the amounts of all species in the aqueous and hydropho-bic phases) generated by the UCD-CACM model. The relevant differences between5

the two models for these compounds are: (i) in the UCD-CACM model the dissocia-tion of the organic acid species contributes to total dissolved H+, but this change doesnot affect the calculation of the inorganic equilibria (Pun et al., 2002); (ii) the activitycoefficients of the organic acid anions are assumed to be the same as those of theundissociated molecule in the UCD-CACM model whereas in AIM they are assigned10

interaction parameters with cations that are the same as those for HSO−4 (for singly

charged anions) or SO2−4 (for doubly charged anions); (iii) the differences in the total

amounts of aerosol water that the models predict – which can be large for situationswhere different solids are present – affect the species amounts in the aqueous fraction.The calculations in this section were carried out to establish the significance of these15

differences, and to verify the UCD-CACM model.We first consider how the surrogate species distribute between the two liquid phases.

Figure 14 shows the calculated fractions of total particulate A1-5 and B1-5 present inthe aqueous phase. Results from the UCD-CACM model show that A1-5 exist almostentirely in the aqueous phase, except for A5 (approx. 96% aqueous) in the later part20

of the cycle. Calculations using AIM, Fig. 14b, show similar partitioning except at thebeginning and middle of the cycle where AIM predicts smaller amounts of aerosol waterthan the UCD-CACM model which reaches its lower limit. At low RH where the aerosoldries out, most of A1-5 would be expected to be in the gas phase. Partitioning resultsfor surrogates B1-5 show that B1 resides almost entirely in the aqueous phase, B325

and B4 in the hydrophobic phase, and B2 and B5 are present in significant amounts inboth phases. Again, the differences between the aqueous fractions predicted by bothmodels and shown in Figs. 14c, d reflect the different amounts of aerosol water, which

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are shown in Fig. 7.Next, results for a single time point at which both models predict similar amounts

of liquid water, and no solids, were examined. Table 1 shows the total amounts, anddegrees of dissociation in the aqueous phase, for all size bins at 08:00 a.m. The reasonthat surrogates A1-5 reside almost entirely in the aqueous phase is partly because5

their activity coefficients in the hydrophobic phase are of the order of 500 to 5000 (notshown in the table), and partly because the total amounts of water solvent in each ofthe aerosol size bins are about two orders of magnitude greater than the sum of theprimary hydrocarbons P1-8 that act as the solvent in the hydrophobic phase. For thiscase the results of the two models are essentially the same for partitioning of A1-510

between the two aerosol phases.Some differences are found for compounds B1-5. The total amounts of B1-5 in the

aqueous phase calculated by the two models are compared as ratios in Fig. 15 at08:00 a.m. for all size bins. The small differences from unity (<3%) for B3-5 reflectdifferences in the total amounts of aerosol water predicted by the two models at this15

RH and can be neglected. For B2, for which AIM predicts up to 19.5% dissociation inbin 15 (see Table 1), the difference in the ratio is up to 9%. It is greatest in the leastacidic size bins for which the degree of dissociation, α in Table 1, is highest. In neutralor alkaline systems we would expect the deviations from unity to be larger still. Theyare primarily due to the different assumptions made regarding the organic anion activity20

coefficients.Surrogates A1, A2, A4, B1 and B2 dissociate in aqueous solution. At 08:00 a.m. the

undissociated fractions exceed 99% of the totals in the aqueous phase in the UCD-CACM model, except for A1 which is 92%. AIM predicts much greater degrees ofdissociation for most of these compounds especially in the less acidic size bins, as25

can be seen in Fig. 16. The greater degree of dissociation predicted by AIM for A1in size bin 15 is due to, first, the formation of HSO−

4 leading to a free H+ molality of0.168 compared to a total (including HSO−

4 ) of 0.629; second, a value of γH+ of 0.29compared to an assumed value of 1.0 in the UCD-CACM model. Consequently the

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activity of H+ in the dissociation calculation (in AIM) is much lower than in the UCD-CACM model. However, compared to other model uncertainties, not least the values ofthe dissociation constants themselves, the effect on SOA yield is minor. It should alsobe remembered that, in the model, partitioning is controlled by mass transfer whichis calculated at each time step, and aerosols – particularly the bins representing the5

larger sizes – can be out of equilibrium with the gas phase. Ratios of equilibriumpartial pressures to actual values in the gas phase, from the UCD-CACM model for08:00 a.m., are compared in Fig. 17. The aerosol contains much less of B1, A2, andA4 (by a factor of ×50 for A2) than required for equilibrium with the gas phase. Theair parcel is still over the ocean at 08:00 a.m., and so the gas phase is interacting10

with the marine background aerosol. The amount of surface area available to facilitategas-to-particle conversion is relatively small, and temperatures low. Wexler and Sein-feld (1991) showed that these conditions promote non-equilibrium behavior in a systeminvolving condensation of inorganic acids and bases. The present case involves con-densation of organic molecules with even smaller diffusion coefficients. It is reasonable15

that equilibrium predictions for gas-to-particle conversion differ from the results of themore realistic dynamic exchange calculation used in the UCD-CACM model.

Next, we compare AIM calculations of full gas/aerosol equilibrium with the results ofthe UCD-CACM model over the complete diurnal cycle, to assess the practical effectof the model differences discussed above. Total moles of particulate primary and sec-20

ondary organic material are shown in Fig. 18. Primaries P1-8 are the same for bothmodels as these species are defined as existing entirely in the particle phase. Totals forsurrogates A1-5 and B1-5 differ most between about 08:00 a.m. and 02:00 p.m. whereAIM predicts the total drying out of the aqueous aerosol phase. The second plot inthe figure shows AIM predictions for a set of simulations in which only (NH4)2SO4(s)25

is able to form, and confirm the requirement for aerosol water for organic surrogatespecies A1-5 to occur in the aerosol. The fractions of total A1-5 and B1-5 present inthe aerosol phase are shown in Fig. 18c. From 08:00 a.m. onwards, 20% or more oftotal A1-5 occurs in the aerosol phase (mostly A2, because of its low vapour pressure),

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but less than 1% of total B1-5.Several conclusions can be drawn from the comparisons here: first, differences be-

tween the amounts of liquid phase water predicted by the models at low RH, relatedto the formation of solids (and the positive lower bound on aerosol water in the UCD-CACM model), strongly influence the aerosol yield of those surrogates that are water5

soluble and do not significantly partition into the hydrophobic phase. Second, the sim-plifications introduced into the UCD-CACM model treatment of the dissociation of theorganic solutes do not have a major effect on overall gas/aerosol partitioning in the ex-ample studied here, although this might not be the case for neutral or alkaline aerosolsystems. Third, dissociation is unlikely to be estimated satisfactorily without an explicit10

treatment of the sulphate/bisulphate equilibrium, and calculated (rather than assumed)activity coefficients of H+

(aq) and organic anions. In the current UCD-CACM model, or-ganic acid dissociation could probably be omitted. Finally, it has been shown earlier,in Fig. 2, that many of the surrogate semi-volatile compounds partition almost entirelyinto one aerosol phase. This offers opportunities for simplifying and increasing the effi-15

ciency gas/aerosol partitioning calculations, by eliminating the liquid/liquid equilibriumcalculation for such compounds.

3.2 Further atmospheric simulations

In this section gas/aerosol partitioning of the primary surrogate organic compounds, theinfluence of the UNIFAC activity coefficients on gas/aerosol partitioning of the semi-20

volatile species, and the effects of variations in po of these compounds, are brieflyexamined. Both AIM and UCD-CACM model simulations are used.

3.2.1 Partitioning of primary organic compounds

Gas/aerosol equilibrium calculations for the diurnal cycle have been repeated, allow-ing primary surrogate compounds P1-7 to partition into the gas phase based upon25

the vapour pressures and enthalpies of vaporisation listed for the model of Nannoolal

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(2007) in Table 5 of Paper II. Although the predicted vapour pressure for P8 is quitehigh, it has been confined to the aerosol phase as it represents the broad class ofmainly hydrocarbon, involatile, material that is found in most aerosols. The resultsare plotted in Fig. 19 as the fraction of the total amount of each surrogate compoundpresent in the aerosol phase. There is significant variation over the course of the5

day. The decrease in the particulate fractions around the middle of the day is partlya response to increased temperature, but mainly to the amounts of P8 available asa solvent. (Fig. 18 shows that these increase by about an order of magnitude from02:00 p.m. to 05:00 p.m. due to anthropogenic emissions.) Less than 1% of the sur-rogates P2 (primary organic di-acids) and P6 (aromatics) are predicted to be in the10

aerosol phase at all times. For P2 this does not seem reasonable, both because di-acids with a larger number of carbon atoms than succinic acid (which is the selectedsurrogate) will have lower vapour pressures, and because the di-acids are water sol-uble. The results are at least qualitatively consistent with the work of Robinson etal. (2007), who argue that most primary organic particulate emissions are semi-volatile.15

3.2.2 The influence of non-ideality in the liquid phase

In Sect. 3.3 of Paper II the variation of the partitioning of water soluble compounds asa function of their sub-cooled vapour pressures was examined. It was assumed thatactivity coefficients in the liquid phase were unity. In the UCD-CACM model UNIFACis used to obtain estimates of activity coefficients for water plus surrogates A1-5 and20

B1-5 in the aqueous phase, and for the surrogates plus primary organics in the hy-drophobic phase. These determine the organic contribution to the total water contentof the aerosol which is small, the partitioning of the surrogates between aqueous andhydrophobic phases, and also influence partitioning between aerosol and gas phases.

What are typical values of the activity coefficients, and to what degree do they control25

partitioning? Table 2 lists mean, minimum and maximum values of the activity coeffi-cients of each surrogate species, in all size bins, over the full diurnal cycle. For mostof these compounds the range of values is not large. For those surrogates occurring

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mainly in the aqueous phase this can be explained by the fact that, unless inorganicsolids form, water will be the major component of the phase. Consequently it is the‘interaction’ with water that will mainly determine the UNIFAC activity coefficient, andnot interactions with other organic species that are present at very low mole fractions.Neither model, as already noted, includes interactions between ions and organic so-5

lutes.The mean values of the activity coefficients listed in Table 2 range from about 1.2 to

almost 2500. The magnitudes of these activity coefficients, combined with the fact thatthey are surrogates for real molecules whose actual composition and structure are onlyapproximately known, suggest that the activity coefficients may be a major source of10

uncertainty in partitioning simulations. To roughly assess this we have carried out cal-culations using AIM in which Raoult’s law (f=1.0) is assumed for the partitioning surro-gate species, but at the same time each species is constrained to exist only in the liquidphase (aqueous, or hydrophobic) in which the full model calculations have suggestedthat it will occur. Thus, A1-5 and B1-2 partition only between the gas and aqueous15

aerosol phases, while B3-5 partition between the gas and hydrophobic aerosol phases.Primary compounds P1-8 are constrained to the hydrophobic phase, as before. Figure20 shows the results of a recalculation of SOA formation, assuming Raoult’s law asnoted above. A comparison of the yields shown in the figure confirms the very largeinfluence of the activity coefficients: in the Raoult’s law case the total yield is enhanced20

by a factor of ×5 or more to 0.5µg m−3 near the end of the cycle when total organicamounts present (gas plus aerosol) are highest. The increase for the B surrogates isgreatest, mainly because of the high value of fB2 in the standard model result (about2.5×103, see Table 2). These results are in contrast to those of Chen et al. (2006)who compared SOA predictions with and without full activity coefficient calculations in25

the eastern United States using the model of Griffin and co-workers. In that study, theactivity coefficients exerted only a small influence, probably due to the dominance ofbiogenic SOA in the simulated aerosol.

The deviations from Raoult’s law calculated for the organic surrogate compounds

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in both phases, and summarised in Table 2, clearly have a significant impact on thecalculated SOA yields as well as controlling the partitioning between aqueous and hy-drophobic phases. The assignment of surrogate compounds in the UCD-CACM modelis generally successful in terms of calculated liquid/liquid phase partitioning – deter-mined by the relative values of fi (aq) and fi (org) in Eq. (1) and the amounts of the solvents5

water and P1-8 – as earlier shown in Fig. 2. However, we have not compared abso-lute values of the activity coefficients of the surrogates and the individual compoundsthey represent. These, combined with po (discussed at the end of Sect. 3.1.2) drivegas/aerosol partitioning.

3.2.3 Variations of subcooled vapour pressures po10

The estimates of vapour pressures of the surrogate compounds presented in Tables 5to 7 of Paper II do not, by themselves, establish the uncertainties associated with thesevapour pressures but do at least suggest minimum ranges. Based upon the estimatederror in the ACD boiling points alone, and neglecting the further uncertainty introducedby the use of the Myrdal and Yalkowsky (1997) equation, the vapour pressures of the15

ten semi-volatile surrogate species have ranges of uncertainty of about ×10 to ×175(highest value divided by the lowest). However, this neglects the fact that the surrogateseach represent groups of compounds that appear to have very wide ranges of vapourpressure, as shown in Table 8 of Paper II.

Together, the results suggest that a comprehensive assessment of the effects of20

vapour pressure uncertainties on SOA yields should involve two types of analysis: first,atmospheric simulations carried out using ranges of probable vapour pressures of thesurrogate compounds, based upon estimates such as those tabulated here. Second,processing the results of atmospheric simulations in a similar way to the diurnal cyclebut calculating gas/aerosol equilibrium for all the individual compounds represented25

by the surrogate species. This is possible with models such as AIM, but the work isoutside the scope of this study. Here we address the first question, and in Fig. 21ashow the predicted 24-h average concentration of SOA in the South Coast Air Basin

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surrounding Los Angeles on 9 September 1993 using the 3D Eulerian version of theUCD-CACM air quality model (Ying et al., 2007; Kleeman et al., 2007). Base casevapour pressures for the surrogate compounds A1-5 and B1-5 are as listed in Tables 6and 7 of Paper II. They differ slightly from those used in previous studies (Kleeman etal., 2007; Ying et al., 2007), because of the correction of errors, but have only a small5

effect on predicted SOA concentrations. In Fig. 21b we show the predicted increasein SOA concentrations that results when lower estimates of the vapour pressures ofthe semi-volatile surrogate species are used in the calculation. These were obtainedby increasing the estimated boiling point of each surrogate compound by the uncer-tainty given by the ACD prediction software and listed on the bottom row of Table 310

of Paper II. As shown in Fig. 21b, predicted SOA concentrations roughly double whenthe lower vapour pressure estimates are used. The greatest increases in predictedSOA concentrations occur in the northern and southern portions of the air basin wherebiogenic SOA is dominant (Kleeman et al., 2007). Further analysis shows that approx-imately 2/3 of the increase in predicted SOA concentrations in the southeast corner15

of the model domain is associated with surrogate species A5 (2-hydroxy-3-isopropyl-6-keto-heptanal), used for CACM species UR7 and UR17 which are produced frombiogenic precursors. The increased SOA concentrations predicted in the vicinity ofClaremont are associated with surrogate species B1 (3,5-dimethyl-2-nitro-4-hydroxy-benzoic acid), B4 (8-hydroxy-11-nitrooxy-hexadecane), A1 (ethanedioic acid), and A220

(2-methyl-5-formyl-2,4-hexadiendioic acid). These comprise compounds that derivefrom anthropogenic PAHs, alkanes, and aromatic hydrocarbons.

4 Discussion

The organic fraction of the aerosol in the UCD-CACM model consists of two broadgroups of compounds: (i) those of a hydrophobic character and made up of long car-25

bon chains with few polar groups, (ii) a set of smaller oxidation products containingone or more polar groups such as –OH and –COOH. The definition of the aerosol

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as containing two liquid phases follows directly from this view. The inorganic and or-ganic components of the aerosol affect each other mainly through the liquid watercontent, which controls the partitioning of the water soluble semi-volatile compounds,and to a lesser extent through the pH of the aqueous portion. Further effects can beexpected from ion-organic interactions (salting-in or salting-out, which affects activity5

coefficients), and from reactions in either liquid phase. The latter are not yet treatedexplicitly in the UCD-CACM model, and the effects of ion-inorganic interactions seemlikely to be smaller than current uncertainties in the vapour pressures of the semi-volatile organic compounds. Below, we summarise the results of this work, and someof the general implications for the development of air quality models.10

4.1 Organic components

Major factors affecting the calculated partitioning of organic compounds, excluding theeffects of chemical reactions and the dynamics of gas/particle exchange, are: (i) theestimation of subcooled liquid vapour pressures po which is discussed in Paper II, (ii)the choice of surrogate compounds and, (iii) their activity coefficients in both aerosol15

phases. The simulation shown in Fig. 21, for decreased vapour pressures of the semi-volatile surrogates consistent with uncertainties in their predicted boiling points, con-firms that these can significantly affect the calculated SOA concentrations (by a factorof two in the example shown).

Semi-volatile compounds were assigned to surrogates in the UCD-CACM model ac-20

cording to structure, source, volatility, and ability to dissociate (for those compoundssoluble in water) (Griffin et al., 2005). The driving force for gas/aerosol partitioningof each organic compound is the product fip

oi , whereas liquid/liquid partitioning within

the aerosol is influenced only by fi (in addition to the quantities of material present inboth phases which determines mole fraction). The comparisons presented in Sect. 3.225

of Paper II show that the estimated vapour pressures of the 38 compounds assignedto the 10 semi-volatile surrogates vary widely, and are not always consistent with thevalue calculated for the surrogate itself, even using only a single estimation method.

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This difficulty seems likely to occur for any model, given the sensitivity of vapour pres-sure to molecular structure and the functional groups present (illustrated in Table 1 ofPaper II for some C4 compounds). One way to address this problem would be to sep-arate the choice of surrogate compounds, and assignment of physical properties forestimating po and for the calculation of activity coefficients, and to base the properties5

of the surrogates more closely on those of the compounds they represent.For example, values of po and ∆Ho

vap for the surrogates could be based upon av-erages of measured or predicted vapour pressures for the individual compounds as-signed to them. They could be grouped, for surrogates used in gas/aerosol partitioningcalculations, according to their vapour pressures (rather than by structure). If the calcu-10

lated vapour pressures listed in Table 8 of Paper II are divided into 10 ranges – one foreach surrogate – then each would include compounds with vapour pressures rangingover a factor of about 5.7 (an increment of 0.65 log10 units). This appears reasonablegiven that the uncertainties in the estimated vapour pressures of the compounds, andtheir current surrogates in the UCD-CACM model, are greater than this.15

In an analogous way, the assignment of individual compounds to surrogates in theaqueous phase could be based upon similarities of the UNIFAC-calculated activity co-efficients for systems of representative composition. In this case, because of the for-mulation of UNIFAC, groupings more directly based upon molecular structure are likely.In the UCD-CACM model the existing assignment of surrogates quite successfully du-20

plicates the liquid/liquid phase partitioning calculated for the individual constituent com-pounds. We have not, however, compared absolute values of the activity coefficientsfor that calculation. They might still vary considerably within the groups assigned toeach surrogate.

There are likely to be difficulties with using more than one assignment of surrogate25

compounds, as this implies changes to the sets of variables used in the phase partition-ing calculation and in the activity coefficients used in the gas/aerosol, and liquid/liquid,elements of the calculation. The approach could not be used in AIM, for example, butmight be possible in the UCD-CACM model because the gas/aerosol partitioning and

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internal aerosol equilibrium calculations are separate. For AIM and similar models itmay be necessary to assign individual compounds to a single set of surrogates, butchosen for similarities in both po and activity coefficients. In this case the significantquantity would be f×po, and the value of f would be the value for the component dis-solved in either water (for those occurring mainly in the aqueous phase), or compound5

P8 (for those occurring mainly in the hydrophobic phase).The dissociation of organic acids (here surrogates A1, A2, A4, B1 and B2) in the

aerosol aqueous phase can potentially affect both the total amounts of the compoundspresent in the aerosol phase, and also aerosol pH. The magnitude of this influencedepends upon (i) the dissociation constants of the organic surrogate compounds; (ii)10

the activity coefficients calculated for, or assigned to, the undissociated organic acidmolecule and organic acid anions, and (iii) the degree to which pH is controlled bythe inorganic electrolytes present. For fogs and cloud water, where solute concentra-tions are low, an expression for the activity coefficients of the organic acid anions thatincludes the Debye-Huckel limiting law is desirable. For example, in AIM the activ-15

ity coefficients of the organic acid anions are determined by analogy with SO2−4(aq) and

HSO−4(aq). In the absence of further information this seems reasonable especially as

the dissociation constants of the surrogate compounds (except for simple dicarboxylicacids), and the compounds they represent, are not well established.

In the simulations presented in this study RH does not exceed 80% and most aerosol20

acidity comes from inorganic components of the aerosol. Although the degrees ofdissociation of B2, and particularly A1, calculated by the UCD-CACM and AIM modelsare very different, the effect on the calculated aerosol burden of SOA is minor as theyare present in only small amounts compared to A2. The treatment of dissociation willbe most important in two situations: where organic acids are the main sources of acidity25

in the aerosol, and in neutral to alkaline cases where dissociation will be greatest. Anexplicit treatment of bisulphate dissociation is also necessary. However, compared tothe effects of uncertainties in vapour pressures of the SOA forming compounds, andthe approximations inherent in using lumped surrogates for partitioning calculations,

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the impact of errors and approximations in the treatment of organic acid dissociationon SOA yield appears to be small.

This study has identified three elements of the gas/aerosol partitioning calculationwhere simplifications in the UCD-CACM model, and therefore gains in efficiency, arepossible. First, the calculation of organic acid dissociation can be neglected. Second,5

it is not necessary to calculate the liquid/liquid partitioning of those organic compoundswhich exist almost entirely in a single liquid phase. Third, the activity coefficients of theorganic compound in the aerosol liquid phases are determined, in both UCD-CACMand AIM models, by interactions with the dominant solvents which are water and P8. Itseems likely that in many simulations the values of the activity coefficients will therefore10

vary little, and in such cases could be determined just once at the beginning of the sim-ulation rather than multiple times during every gas/aerosol and liquid/liquid partitioningcalculation.

4.2 Inorganic components

As noted above, the influence of the inorganic electrolyte content of the aerosol parti-15

tioning of the semi-volatile SOA compounds is exerted mainly via aerosol water con-tent: the relationship between water activity (RH) and concentration at moderate tohigh RH, and the formation of solids at low RH leading to the eventual efflorescence(drying out) of the aerosol.

There are significant differences between most of the inorganic thermodynamic mod-20

ules in current use, and we have compared the differences between the UCD-CACMmodel and AIM in some detail. The UCD-CACM model has dynamically controlledpartitioning between the gas phase and 15 aerosol size bins (of which only the largest10 have been considered here), and with lower limits to the amount of aerosol wa-ter set for each bin. In contrast, AIM is a bulk equilibrium thermodynamic model with25

a more complex treatment of aqueous mixtures, no lower limit to the aerosol wateramount, and a larger set of possible solids. However, it is clear from the comparisonsshown in Sect. 3.1.1 that the effects of these differences on the calculated amounts of

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aerosol, and the partitioning of both organic compounds and the key volatile inorganiccompounds NH3 and HNO3, is often small.

The effects of the differences between the models are greatest under conditionswhere the aerosol is predicted by AIM to contain little or no liquid water. This occursin the afternoon of the diurnal cycle (when the RH is lowest) and virtually all the wa-5

ter soluble SOA material is returned to the gas phase in the AIM simulation. In theUCD-CACM model the aerosol water does not fall below an assigned lower limit (seeFigs. 7 and 11), resulting in the retention of the water soluble organic compounds. Thisretention is also seen in the atmosphere – probably for other reasons – and the useof a lower limit to aerosol water is an artificial constraint within the model. It would be10

preferable to directly model either metastable aqueous aerosols, which are supersatu-rated with respect to the solids that might form, or the equilibrium state of the aerosolwhich is allowed to dry out completely at low RH.

The differences between the inorganic models, in terms of HNO3 and NH3 partition-ing, are less in the simulated diurnal cycle than might be expected from the analysis in15

Sect. 3.1.1. This is because the aerosol is largely acidic until the early afternoon, andpNH3 negligibly low, but an injection of NH3 as the parcel passes over a region of inten-sive farming results in the air parcel being dominated by this species, which is mostlyin the gas phase. Consequently, in the latter part of the day even large changes in thetotal ammonia present in the aerosol have only a small influence on the amount in the20

gas phase. Under atmospheric conditions where the partitioning of both HNO3 andNH3 is more evenly balanced between both phases, differences between the inorganicthermodynamic models would be more apparent. It is worth noting that neither AIMnor other current models include the influences of dissolved ions on the activity coeffi-cient of aqueous NH3, which directly affects the calculated partial pressure. This is in25

spite of the fact that data for at least some of the main aerosol components, including(NH4)2SO4 and NaCl, have been available for some time (Clegg and Brimblecombe,1989). For example, the value of γNH3 in aqueous (NH4)2SO4 ranges from 1.16 at98% RH, to 1.96 at 90% and 2.68 at 80% RH. The fact that these activity coefficients

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are greater than unity means that the amounts of NH3 in the gas phase will be under-predicted for aerosols that are neutral or alkaline by models that assume γNH3=1.

4.3 Future developments

The physical properties of polar multifunctional organic compounds, such as those thatmake up SOA, are among the most difficult to predict. This is reflected in the results5

in Paper II, where the wide variations in estimated po add a significant uncertainty tothe calculated gas/aerosol partitioning at moderate to low RH. While models basedupon an explicit chemistry must remain consistent with the known properties of thecompounds, these uncertainties are large enough – and unlikely to decrease much inthe near future – that field data and the results of laboratory studies of SOA formation10

are still needed to optimize the models. To some extent this is already done: thetreatment of SOA formation in CMAQ is based directly upon chamber studies of SOAformation (Yu et al., 2007) and in the UCD-CACM model the vapour pressures of theten SOA surrogates have been adjusted to be consistent with chamber measurementsof aerosol formation from aromatic and monoterpene oxidation (Griffin et al., 2005).15

It also seems likely that further advances in explicit models will come more fromlaboratory and field measurements than from improved predictive techniques for eithervapour pressures, or from activity coefficient models that better integrate the treatmentsof inorganic and uncharged organic components of the aerosol. While dissolved saltsundoubtedly influence the activities of dissolved organic compounds (and vice versa),20

uncertainties in the vapour pressures of the organic compounds appear to be largecompared to the probable effects on activity coefficients. Except where salt-organicinteractions induce a qualitative change in behaviour, promoting a chemical reaction orinducing a phase separation for example, the current relatively simple treatment of thethermodynamics of the aqueous aerosol phase for inorganic/organic mixtures seems25

justified. We note that the observed lowering of the deliquescence RH of mixturesof inorganic and organic solutes is reasonably approximated by the influence of bothsolutes on the water activity of the mixture (see references in Clegg and Seinfeld,

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2006a, b), and that this effect is reproduced by both the ZSR relationship (used in theUCD-CACM and other models) and in AIM using the approach described by Clegg etal. (2001).

Future studies with the UCD-CACM model will include revisions to the assignmentsof compounds to surrogate species and the vapour pressures of the surrogates. Clearly5

an explicit representation of oligomer formation is also desirable as data describing theparent compounds and rate limiting steps in the formation process become available.

Appendix A

The surrogate compounds

The molecular structures of the eighteen surrogate compounds in the UCD-CACM10

model are as given by Griffin et al. (2003), except that compound B5 (S10 in Fig. 1of Griffin et al., 2003) has been corrected as described by Griffin et al. (2005). Thehopane, compound P5, differs from the structure for CAS Registry number 471-62-5only in the position of one -CH3 group and the latter is assumed here. The structureof B5 is shown in Fig. 22 below. Formulae, CAS Registry numbers and molar masses15

are as follows: C2H2O4, 144-62-7, 90.3 g (A1); C8H8O5, 538367-55-4, 184.2 g (A2);C8H10O3, 538367-56-5, 154.2 g (A3); C9H14O4, 538367-57-6, 186.2 g (A4); C10H18O3,538367-58-7, 186.3 g (A5); C9H9NO5, 538367-59-8, 211.2 g (B1); C10H10O3, 538367-60-1, 178.2 g (B2); C12H11NO3, 538367-61-2, 217.2 g (B3); C16H33NO4, 538367-62-3,303.4 g (B4); C10H19NO4, 217.3 g (B5, corrected); C29H60, 630-03-5, 408.8 g (P1);20

C4H6O4, 110-15-6, 118.1 g (P2); C12H8O4, 1141-38-4, 216.2 g (P3); C22H12, 191-24-2, 276.3 g (P4); C30H52, 471-62-5, 412.7 g (P5); C8H6O4, 88-99-3, 166.1 g (P6);C18H36O2, 57-11-4, 284.5 g (P7); C28H54, 538367-70-3, 390.7 g (P8).

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Dissociation constants

Dissociation of the semi-volatile organic surrogates containing -COOH groups(s) iscalculated using dissociation constants Kd1 and Kd2 defined in Eqs. (3a) and (3b).The following values are given in units of mol kg−1, and the equilibrium constants areassumed not to vary with temperature: 1.70×10−3 (Kd1 for B1), 7.33×10−5 (Kd1 for5

B2), 5.4×10−2 (Kd1 for A1), 5.2×10−5 (Kd2 for A1), 3.7×10−5 (Kd1 for A2), 3.9×10−6

(Kd2 for A2), 6.52×10−4 (Kd1 for A4).

UNIFAC group definitions of the surrogate compounds

For UNIFAC calculations of the activity coefficients in liquid mixtures the organic com-ponents are defined in terms of the structural groups of which they are composed (and10

without regard to position). The UNIFAC groups that occur in compounds P1-8, A1-5and B1-5 are listed in Table 3 below. There is no UNIFAC -O-NO2 group such as oc-curs in compounds B3-5. We have therefore assumed the composition -CH2-NO2 foractivity coefficient calculations. The UNIFAC definitions of all of the surrogate speciesare given in Table 4.15

Estimation of vapour pressures of the surrogate compounds

The vapour pressures of the surrogate compounds estimated using the Myrdal andYalkowsky (1997) equation, and listed in Tables 5–7 of Paper II, require boiling pointsat atmospheric pressure, a structural parameter τ, and a hydrogen bonding numberHBN. In earlier versions of the UCD-CACM model there were some errors in these20

parameters. The correct values are listed in Table 9 of Paper II.

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Appendix B

Some of the largest differences between the UCD-CACM and extended AIM inor-ganic thermodynamic treatments occur in the calculated equilibrium partial pressuresof the inorganic gases HNO3 and NH3 shown in Fig. 10, and are analysed here. Thegas/liquid equilibrium of HNO3 and NH3 are described, on the molality scale, by:5

KH (HNO3)=aH+aNO−3/pHNO3 (1a)

= mH+mNO−3γH+γNO−

3/pHNO3 (1b)

= mH+mNO−3γHNO2

3/pHNO3 (1c)

K ′H (NH3)=aNH+

4/(aH+pNH3) (2a)

= mNH+4 (γNH+

4/γH+)/(mH+pNH3) (2b)10

where prefix a denotes activity, m molality, and γi is the activity coefficientof ion i . Symbol KH (HNO3) is the molality based Henry’s law constant ofHNO3 (2.63×10−6 mol2 kg−2 atm−1 at 298.15 K, Carslaw et al., 1995), and K ′

H (NH3)(1.066×10−11 atm−1 at 298.15 K) is an equilibrium constant equivalent to the Henry’slaw constant of NH3 divided by the acid dissociation constant of NH+

4(aq). The mean15

activity coefficient of HNO3, γHNO3, is equal to the square root of the product (γH+

γNO−3 ). Note that in the acidic solutions in this example the dissociation of NH+

4(aq) toNH3(aq) is small and can be neglected.

It is clear from the above equations that the differences between the predictions ofthe two models will be mainly caused by differences in aH+: a lower value predicted20

by AIM results in both a smaller equilibrium pHNO3 and a higher pNH3 according tothe equations above. Figure 9 of Wexler and Seinfeld (1991) shows that stoichiometricactivity coefficients of aqueous H2SO4 are not well reproduced by that model. However,the main reason for the differences in predicted vapour pressures is likely to be the fact

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that the H+(aq)+ SO2−

4(aq) ↔ HSO−4(aq) equilibrium is not recognized in the Kusik and

Meissner equations used to predict inorganic activities in the UCD-CACM model. Thisis verified, below, by comparing both models to laboratory data.

Maeda and Iwata (1997) have measured the acid dissociation constant of NH+4(aq)

in aqueous (NH4)2SO4, on a total hydrogen ion basis, at 25◦C. These measurements5

can be used as a test of the models’ ability to represent activities of H+(aq) in solutions

containing mainly (NH4)2SO4 such as the aerosols in the larger size bins in Fig. 10.The experimental molal dissociation constants in Table 1 of Maeda and Iwata, Ka,m,are equivalent to:

Ka,m = (mH+ +mHSO−4 )mNH3/mNH+

4 (3)10

Introducing the thermodynamic dissociation constant of HSO−4(aq), K

oa (HSO4), Eq. (6)

can be rewritten:

Ka,m = (mH+mNH3/mNH+4 )[1 + (m/K o

a (HSO4))(γH+γSO2−4 )/γHSO−

4 ] (4)

where m is the molality of (NH4)2SO4 and K oa (HSO4) has a value of 0.0105 mol kg−1

at 25◦C (Clegg et al., 1994). The stoichiometric dissociation constant on a free H+ ion15

basis (the first term in parentheses in Eq. 4), is equivalent to K oa,m×γNH+

4 /(γH+γNH3)where K o

a,m is the thermodynamic value of the dissociation constant which is5.6885×10−10 mol kg−1 at 25◦C (Bates and Pinching, 1949). Substituting into Eq. (4)we obtain an expression for the reciprocal γNH+

4 /γH+ in the solution in terms only of mand the activity coefficients of the other species present:20

(γNH+4/γH+) = (Ka,m/K

oa,m)γNH3/[1 + (m/K o

a (HSO4))(γH+γSO2−4 )/γHSO−

4 ] (5)

Maeda and Iwata (1997) have shown that their experimental Ka,m can be satisfac-torily reproduced using a molality-based Pitzer activity coefficient model (Pitzer, 1991)using interaction parameters determined by Clegg and co-workers (Clegg and Brimble-combe, 1989; Clegg and Whitfield, 1992) from extensive experimental data for activity25

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coefficients, solubilities and osmotic coefficients. We have used this model, togetherwith Eq. (5) to obtain values of (γNH+

4 /γH+) from the Ka,m tabulated by Maeda andIwata. Given that the value of γNH+

4 is determined by interactions with SO2−4 in aque-

ous (NH4)2SO4, and therefore known from data for the pure aqueous salt, comparisonsof the modelled and experimental (γNH+

4 /γH+) are essentially a test of the models’5

ability to predict γH+ which is central to the differences between the predicted vapourpressures shown in Fig. 10 and discussed above. We note that it is not possible topredict Ka,m directly with the UCD-CACM model because neither HSO−

4(aq) nor NH3(aq)

are included as individual species. This lack of NH3 makes the model most applicableto atmospheric systems in which the aerosols are acidic.10

Values of (γNH+4 /γH+) in aqueous (NH4)2SO4 were calculated directly using AIM,

recalling that the value of the reciprocal is the same on both the molality and molefraction scales. The quantity was obtained from the UCD-CACM model by making useof the following relationships:

γ(NH4)2SO4 = [(γNH+4 )2γSO4]1/3 (6)15

γH2SO4 = [(γH+)2γ SO2−4 ]1/3 (7)

(γNH+4/γH+) = (γ(NH4)2SO4/γH2SO4)3/2 (8)

Values of the reciprocal calculated by all three models are compared with those de-rived from the experimental data in Fig. 23. The molality-based model closely agreeswith the measurements, as shown by Maeda and Iwata (1997), and AIM agrees rea-20

sonably well, though with a small positive deviation. However, the Kusik and Meissnerthermodynamic approach yields a decrease in (γNH+

4 /γH+) – the opposite trend to thatobserved – and at 6 mol kg−1 (80% RH) the two models differ by a factor of about 6.9.The results in the figure are consistent with the differences in predicted equilibriumpHNO3 and pNH3 in Fig. 8: values of (γNH+

4 /γH+) that are too low lead to a pressure25

ratio for NH3 that is too high and a ratio for HNO3 that is too low.11012




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Acknowledgements. This research was supported by U.S. Environmental Protection Agencygrant RD-831082 and Cooperative Agreement CR-831194001, by the Natural EnvironmentResearch Council of the UK (as a part of the Tropospheric Organic Chemistry Experiment,TORCH), and by the European Commission as part of EUCAARI (European Integrated Projecton Aerosol Cloud, Climate and Air Quality Interactions). The work has not been subject to the5

U.S. EPA’s peer and policy review, and does not necessarily reflect the views of the Agency andno official endorsement should be inferred. The authors would like to thank the AtmosphericSciences Modelling Division (ASMD) of U.S. EPA for hosting S. L. Clegg while carrying out thisstudy, and Prakash Bhave and other ASMD members for helpful discussions.

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Table 1. Total Amounts (µmol m−3) of Anthropogenic and Biogenic Surrogates in Both AerosolPhases, and their Degrees of Dissocation (α) in the Aqueous Phase Calculated Using AIM.

Bin H20 B1(aq) α B2(aq) α B3(aq) B4(aq) B5(aq)

6 8.81E-02 2.12E-07 0.0002 4.49E-09 0.0008 3.09E-12 1.02E-10 3.69E-127 8.98E-02 2.17E-07 0.0007 4.53E-09 0.0028 3.02E-12 9.99E-11 3.63E-128 1.44E-01 3.43E-07 0.0038 7.32E-09 0.0162 4.88E-12 1.61E-10 5.89E-129 1.30E-01 3.00E-07 0.0062 6.60E-09 0.0262 4.41E-12 1.46E-10 5.34E-1210 9.12E-02 1.98E-07 0.0088 4.63E-09 0.0368 3.10E-12 1.03E-10 3.74E-1211 4.89E-02 9.45E-08 0.0265 2.53E-09 0.1050 1.69E-12 5.61E-11 2.03E-1212 2.79E-02 4.29E-08 0.0420 1.43E-09 0.1590 9.67E-13 3.20E-11 1.16E-1213 1.74E-02 2.36E-08 0.0428 9.20E-10 0.1618 6.01E-13 1.97E-11 7.20E-1314 1.04E-02 1.16E-08 0.0472 5.70E-10 0.1760 3.61E-13 1.11E-11 4.33E-1315 4.57E-03 2.97E-09 0.0531 2.52E-10 0.1946 1.58E-13 4.19E-12 1.89E-13

Bin A1 (aq) α A2(aq) α A3(aq) A4(aq) α A5(aq)

6 1.02E-08 0.0061 3.82E-06 0.0000 8.17E-09 2.64E-08 0.0001 6.11E-087 1.04E-08 0.0200 3.29E-06 0.0000 8.35E-09 2.69E-08 0.0003 6.24E-088 1.68E-08 0.1072 3.59E-06 0.0001 1.35E-08 4.22E-08 0.0015 1.01E-079 1.51E-08 0.1648 2.42E-06 0.0001 1.21E-08 3.69E-08 0.0024 9.05E-0810 1.06E-08 0.2195 1.18E-06 0.0002 8.50E-09 2.48E-08 0.0034 6.35E-0811 5.68E-09 0.4709 3.95E-07 0.0006 4.57E-09 1.17E-08 0.0103 3.41E-0812 3.30E-09 0.5952 1.22E-07 0.0010 2.60E-09 5.23E-09 0.0165 1.94E-0813 2.06E-09 0.6005 5.76E-08 0.0010 1.61E-09 2.65E-09 0.0169 1.21E-0814 1.24E-09 0.6261 2.37E-08 0.0011 9.56E-10 1.13E-09 0.0186 7.26E-0915 5.03E-10 0.6567 4.86E-09 0.0012 3.96E-10 2.63E-10 0.0210 3.05E-09

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Bin Σ P1-8 B1(org) B2(org) B3(org) B4(org) B5(org)

6 1.11E-3 1.71E-10 2.38E-09 2.19E-08 1.08E-06 3.21E-117 6.54E-4 9.95E-11 1.40E-09 1.25E-08 5.99E-07 1.79E-118 3.63E-4 4.59E-11 7.12E-10 6.45E-09 2.84E-07 8.55E-129 1.81E-4 1.88E-11 3.25E-10 3.00E-09 1.21E-07 3.66E-1210 2.30E-4 2.64E-11 4.40E-10 4.10E-09 1.81E-07 5.43E-1211 2.68E-4 2.91E-11 4.99E-10 4.99E-09 2.32E-07 6.91E-1212 5.30E-5 2.99E-12 7.61E-11 8.24E-10 3.08E-08 9.21E-1313 1.74E-4 8.70E-12 2.58E-10 2.71E-09 1.00E-07 3.03E-1214 2.09E-4 8.47E-12 3.14E-10 3.25E-09 1.13E-07 3.64E-1215 9.17E-5 2.15E-12 1.36E-10 1.42E-09 4.27E-08 1.59E-12

Bin A1(org) A2(org) A3(org) A4(org) A5(org)

6 3.41E-13 5.82E-10 4.09E-12 8.42E-12 3.78E-107 2.02E-13 2.89E-10 2.37E-12 4.84E-12 2.18E-108 9.49E-14 9.69E-11 1.11E-12 2.17E-12 1.01E-109 4.13E-14 3.23E-11 4.71E-13 8.83E-13 4.25E-1110 5.23E-14 3.17E-11 7.04E-13 1.28E-12 6.41E-1111 4.21E-14 2.42E-11 8.91E-13 1.43E-12 8.17E-1112 5.50E-15 1.97E-12 1.16E-13 1.40E-13 1.04E-1113 1.79E-14 4.94E-12 3.81E-13 3.76E-13 3.44E-1114 2.01E-14 4.05E-12 4.52E-13 3.20E-13 4.12E-1115 7.50E-12 8.32E-13 1.87E-13 7.42E-14 1.73E-11

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Table 2. Ranges of Activity Coefficients of Surrogate Species A1-5, B1-5, in All Size Bins.

Species Mean fi Range Principal Phase

A1 1.16 1.14–1.18 aqueousA2 13.2 11.3–14.2 aqueousA3 49.9 41.2–54.8 aqueousA4 38.9 32.5–42.1 aqueousA5 187 153–204 aqueousB1 131 105–152 aqueousB2 2485 1906–2792 aqueousB3 16.7 13.9–19.2 hydrophobicB4 29.2 20.3–37.2 hydrophobicB5 57.1 39.7–73.4 hydrophobic

Notes: values of the mole fraction activity coefficients fi of each surrogate i are for all size binsand for all times over the diurnal cycle. The geometric mean is listed.

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Table 3. UNIFAC Groups and Examples of Their Use.

Group No. Name Example

11 CH3 ethane: 2CH312 CH2 n-butane: 2CH3, 2CH213 CH isobutane: 3CH3,1CH14 C neopentane: 4CH3, 1C24 CH=C 2-methyl-2-butene: 2CH3, 1CH=C25 C=C 2,3-dimethylbutene: 4CH3, 1C=C31 ACH napthalene: 8ACH, 2AC32 AC styrene: 1CH2 = CH, 5ACH, 1AC41 ACCH3 toluene: 5ACH, 1ACCH342 ACCH2 ethylbenzene: 5ACH, 1ACCH2, 1CH350 OH propanol-2: 2CH3, 1CH, 1OH70 H20 water: 1H2O80 ACOH phenol: 5ACH, 1ACOH91 CH3CO butanone: 1CH3, 1CH2, 1CH3CO92 CH2CO pentanone-3: 2CH3, 1CH2, 1CH2CO100 CHO propionaldehyde: 1CH3, 1CH2, 1CHO201 COOH acetic acid: 1CH3, 1COOH262 CH2NO2 propane-1-nitro: 1CH3, 1CH2, 1CH2NO2270 ACN02 benzene-nitro: 5ACH, 1ACNO2

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Table 4. UNIFAC Group Definitions of Surrogate Compounds.

Compound Group # Group # Group # Group # Group # Group #

water 70 1P1 11 2 12 27P2 12 2 201 2P3 32 4 31 6 201 2P4 32 10 31 12P5 11 8 12 11 13 6 14 5P6 31 4 32 2 201 2P7 11 1 12 16 201 1P8 11 12 12 6 13 6 14 4B1 (S6) 31 1 32 1 80 1 201 1 41 2 270 1B2 (S7) 201 1 100 1 32 2 31 2 41 2B3 (S8) 31 6 32 2 41 1 42 1 262 1B4 (S9) 50 1 11 2 12 12 13 2 262 1B5 (S10) 11 3 12 3 13 3 50 1 14 1 262 1A1 (S1) 201 2A2 (S2) 201 2 100 1 24 2 11 1A3 (S3) 11 2 100 2 50 1 24 1 25 1A4 (S4) 50 1 201 1 91 1 11 2 13 2 24 1A5 (S5) 91 1 12 2 13 3 11 2 50 1 100 1

Notes: the structures are as given by Griffin et al. (2003), with the exception of the correctionshown in Fig. 22 for B5. The substitution of –CH2–NO2 for –O–NO2 is noted in the text.

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Figure 1. Production and gas to aerosol partitioning of organic compounds, based upon the scheme proposed by Pun et al. (2002). The aerosol particle on the right hand side contains an upper aqueous portion and lower hydrophobic (organic) phase. Gas phase reactions and emissions on the left hand side produce solid material or involatile products (grouped into primary compounds P1 to P8 in the UCD-CACM model) which are assigned in step (a) directly to the hydrophobic aerosol phase. Partitioning into the gas phase is possible for at least some of these compounds, step (f), but is not included in the UCD-CACM model. Semi-volatile compounds produced in the gas phase are grouped into a smaller number of surrogate species (38 compounds are assigned to surrogates A1 to A5, and B1 to B5, in the UCD-CACM model). These are allowed to partition between the gas phase and both aqueous and hydrophobic phases in the aerosol, in step (b). Equilibrium between the two aerosol phases, step (c), is calculated. Surrogates containing –COOH groups can dissociate in the aqueous phase, step (d). Reactions, step (e), in the aerosol phases may sequester semi-volatile compounds in the condensed phase. Such reactions are not included explicitly in the UCD-CACM model.

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Fig. 1. Production and gas to aerosol partitioning of organic compounds, based upon thescheme proposed by Pun et al. (2002). The aerosol particle on the right hand side containsan upper aqueous portion and lower hydrophobic (organic) phase. Gas phase reactions andemissions on the left hand side produce solid material or involatile products (grouped intoprimary compounds P1 to P8 in the UCD-CACM model) which are assigned in step (a) directlyto the hydrophobic aerosol phase. Partitioning into the gas phase is possible for at least someof these compounds, step (f), but is not included in the UCD-CACM model. Semi-volatilecompounds produced in the gas phase are grouped into a smaller number of surrogate species(38 compounds are assigned to surrogates A1 to A5, and B1 to B5, in the UCD-CACM model).These are allowed to partition between the gas phase and both aqueous and hydrophobicphases in the aerosol, in step (b). Equilibrium between the two aerosol phases, step (c), iscalculated. Surrogates containing –COOH groups can dissociate in the aqueous phase, step(d). Reactions, step (e), in the aerosol phases may sequester semi-volatile compounds in thecondensed phase. Such reactions are not included explicitly in the UCD-CACM model.

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Figure 2. Calculated fractional partitioning of 0.01 moles of surrogates B1-5, A1-5, and the 38 compounds assigned to them, in a system containing 1 mole of water and 1 mole of P8. Solid vertical lines show partitioning of the individual components. For example, about 0.95 (95%) of component 1 (upper x-axis) is present in the hydrophobic P8 phase at equilibrium, and a fraction of 0.05 (5%) in the aqueous phase. The hatched boxes indicate the calculated partitioning of the surrogates (lower x-axis) to which the individual compounds are assigned. For example, over 95% of B1 is calculated to occur in the aqueous phase, whereas the three components assigned to it are present mainly in the hydrophobic phase. The component assignments are given in the notes to Table 8 of Paper II.

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Fig. 2. Calculated fractional partitioning of 0.01 moles of surrogates B1-5, A1-5, and the 38compounds assigned to them, in a system containing 1 mole of water and 1 mole of P8. Solidvertical lines show partitioning of the individual components. For example, about 0.95 (95%) ofcomponent 1 (upper x-axis) is present in the hydrophobic P8 phase at equilibrium, and a frac-tion of 0.05 (5%) in the aqueous phase. The hatched boxes indicate the calculated partitioningof the surrogates (lower x-axis) to which the individual compounds are assigned. For example,over 95% of B1 is calculated to occur in the aqueous phase, whereas the three componentsassigned to it are present mainly in the hydrophobic phase. The component assignments aregiven in the notes to Table 8 of Paper II.

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Fig. 3. Calculated trajectory path for the air parcel arriving at Claremont CA at 12:00 PST on 9September 1993.

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Figure 4. Inorganic composition of the air parcel in mol m-3, over the diurnal cycle on 8 September 1993 shown in Fig. 3. Amounts are plotted above each other so that the vertical extent of each of the four areas corresponds to the amount of that species present, e.g., the amount of SO4

2- at time zero in both plots is about 0.6×10-7 mol m-3. The amount of chloride present in the system on these scales is negligible and not shown, and the areas marked NH4 are total ammonia (NH4

+ and NH3). (a) Total amounts in the aerosol and gas phases; (b) amounts present in the aerosol (UCD-CACM model results).

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Fig. 4. Inorganic composition of the air parcel in mol m−3, over the diurnal cycle on 8 September1993 shown in Fig. 3. Amounts are plotted above each other so that the vertical extent of eachof the four areas corresponds to the amount of that species present, e.g., the amount of SO2−

4 attime zero in both plots is about 0.6×10−7 mol m−3. The amount of chloride present in the systemon these scales is negligible and not shown, and the areas marked NH4 are total ammonia (NH+

4and NH3). (a) Total amounts in the aerosol and gas phases; (b) amounts present in the aerosol(UCD-CACM model results).

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Figure 5. Total amounts (mol m-3) in the gas and aerosol phases of each of the semi-volatile surrogate species during the simulated diurnal cycle. (a) B1-5; (b) A1-5.

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Fig. 5. Total amounts (mol m−3) in the gas and aerosol phases of each of the semi-volatilesurrogate species during the simulated diurnal cycle. (a) B1-5; (b) A1-5.

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Figure 6. Atmospheric temperature (solid line, left axis) and relative humidity (dashed line, right axis) from ground level to 38 m, for the trajectory shown in Fig. 3.

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Fig. 6. Atmospheric temperature (solid line, left axis) and relative humidity (dashed line, rightaxis) from ground level to 38 m, for the trajectory shown in Fig. 3.

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Figure 7. (a) Total moles of water (nH2O) in the aerosol phase, per m3 of atmosphere, for size bins 6 to 15. Solid line – AIM model; dashed line and open circle – UCD-CACM model, based upon the total moles of solutes in each bin predicted by the UCD-CACM model. (b) Moles of inorganic solutes calculated by AIM for each aerosol size bin, summed. Dots – (NH4)2SO4(s); open circles - (NH4)2SO4(s) plus letovicite; plus - (NH4)2SO4(s) plus the double salt (d.s.) 2NH4NO3.(NH4)2SO4(s). At time 0:00 there are about 1.7×10-8 moles of (NH4)2SO4(s) and 1.9×10-8 moles of letovicite.

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Fig. 7. (a) Total moles of water (nH2O) in the aerosol phase, per m3 of atmosphere, for sizebins 6 to 15. Solid line – AIM model; dashed line and open circle – UCD-CACM model, basedupon the total moles of solutes in each bin predicted by the UCD-CACM model. (b) Moles of in-organic solids calculated by AIM for each aerosol size bin, summed. Dots – (NH4)2SO4(s);open circles – (NH4)2SO4(s) plus letovicite; plus – (NH4)2SO4(s) and the double salt (d.s.)

2NH4NO3.(NH4)2SO4(s). At time 0:00 there are about 1.7×10−8 moles of (NH4)2SO4(s) and

1.9×10−8 moles of letovicite.

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Figure 8. Total water (nH2O) in the aerosol phase, per m3 of atmosphere, for each of size bins 6 to 15, at 8 am. Solid line - UCD-CACM model; dashed line and open circle – AIM model for the total moles of solutes in each bin predicted by the UCD-CACM model.

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Fig. 8. Total moles of water (nH2O) in the aerosol phase, per m3 of atmosphere, for each ofsize bins 6 to 15, at 08:00 a.m. Solid line – UCD-CACM model; dashed line and open circle –AIM model for the total moles of solutes in each bin predicted by the UCD-CACM model.

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Figure 9. The inorganic composition of each aerosol size bin at time 8 am. (a) Amounts of NH4

+, SO42- and H+; (b) amount of NO3- (reduced scale).

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Fig. 9. The inorganic composition of each aerosol size bin at time 08:00 a.m. predicted by theUCD-CACM model. (a) Amounts of NH+

4 , SO2−4 and H+; (b) amount of NO−

3 (reduced scale).

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Figure 10. (a) The equilibrium partial pressures of NH3 and HNO3 over each aerosol size bin calculated by AIM, divided by the actual partial pressures in the gas phase from the UCD-CACM model or by the equilibrium values calculated by the UCD-CACM model for the same aerosol compositions. Dot and solid line – NH3, for the UCD-CACM calculated equilibrium partial pressure; open circle and dotted line – NH3, for the actual gas phase amount in the UCD-CACM model result; plus and solid line – HNO3, for the UCD-CACM calculated equilibrium partial pressure; open square and solid line – HNO3, for the actual gas phase amount in the UCD-CACM model result. (b) Aerosol composition, expressed as the fractional contributions (on a molar basis) of (NH4)2SO4, H2SO4 and HNO3.

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Fig. 10. (a) The equilibrium partial pressures of NH3 and HNO3 over each aerosol size bincalculated by AIM, divided by the actual partial pressures in the gas phase from the UCD-CACM model and the equilibrium values calculated by the UCD-CACM model for the sameaerosol compositions. Dot and solid line – NH3, for the UCD-CACM calculated equilibriumpartial pressure; open circle and dotted line – NH3, for the actual gas phase amount in theUCD-CACM model result; plus and solid line – HNO3, for the UCD-CACM calculated equilibriumpartial pressure; open square and solid line – HNO3, for the actual gas phase amount in theUCD-CACM model result. (b) Aerosol composition, expressed as the fractional contributions(on a molar basis) of (NH4)2SO4, H2SO4 and HNO3.

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Figure 11. Calculated aerosol water content, per m3 of atmosphere, over the diurnal cycle. Open circle and dashed lines – results from the UCD-CACM model, as shown in Fig. 7; dot and solid line – the result from AIM for a gas/aerosol equilibrium partitioning calculation including all species and an aggregate composition equal to the total amounts of each species in the gas phase and in size bins 6-15; small dot and dash-dot line – result from AIM but where (NH4)2SO4(s) is the only solid allowed to form.

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Fig. 11. Calculated aerosol water content, per m3 of atmosphere, over the diurnal cycle. Opencircle and dashed lines – results from the UCD-CACM model, as shown in Fig. 7; dot andsolid line – the result from AIM for a gas/aerosol equilibrium partitioning calculation includingall species and an aggregate composition equal to the total amounts of each species in thegas phase and in size bins 6–15; small dot and dash-dot line – result from AIM but where(NH4)2SO4(s) is the only solid allowed to form.

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Figure 12. Moles of inorganic solids calculated by AIM over the diurnal cycle. Note that, for the aggregated aerosol composition modelled for this case, the double salt seen in Fig. 7 does not occur. Dots – (NH4)2SO4(s); open circles - (NH4)2SO4(s) plus letovicite. The dashed line shows the amounts of (NH4)2SO4(s) predicted if letovicite is prevented from forming.

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Fig. 12. Moles of inorganic solids calculated by AIM over the diurnal cycle. Note that, for theaggregated aerosol composition modelled for this case, the double salt seen in Fig. 7 does notoccur. Dots – (NH4)2SO4(s); open circles - (NH4)2SO4(s) plus letovicite. The dashed line showsthe amounts of (NH4)2SO4(s) predicted if letovicite is prevented from forming.

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Figure 13. Calculated partial pressures of HNO3 and NH3 in the gas phase, over the diurnal cycle. Open circle and dashed line – amounts of HNO3 from the UCD-CACM model result; dot and solid line – amounts of HNO3 from the AIM gas/aerosol equilibrium calculation. Open square and dashed line - amounts of NH3 from the UCD-CACM model result; solid square and line – amounts of NH3 from the AIM gas/aerosol equilibrium calculation. The dotted line (a) indicates the AIM result for pNH3 where only the solid (NH4)2SO4(s) can form. (Except for the period 8 am to 1 pm this differs negligibly from the main result shown). The vertical lines from midnight to 1 pm show the range of equilibrium partial pressures over size bins 8-16 (UCD-CACM model) to indicate the degree of disequilibrium between the gas phase and larger aerosol size bins. After 1 pm, and for HNO3 at all times, the range is small and close to the actual partial pressure and is not shown.

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Fig. 13. Calculated partial pressures of HNO3 and NH3 in the gas phase, over the diurnal cycle.Open circle and dashed line – amounts of HNO3 from the UCD-CACM model result; dot andsolid line – amounts of HNO3 from the AIM gas/aerosol equilibrium calculation. Open squareand dashed line – amounts of NH3 from the UCD-CACM model result; solid square and line –amounts of NH3 from the AIM gas/aerosol equilibrium calculation. The dotted line (a) indicatesthe AIM result for pNH3 where only the solid (NH4)2SO4(s) can form. (Except for the period08:00 a.m. to 01:00 p.m. this differs negligibly from the main result shown). The vertical linesfrom midnight to 01:00 p.m. show the range of equilibrium partial pressures over size bins 8–16(UCD-CACM model) to indicate the degree of disequilibrium between the gas phase and largeraerosol size bins. After 01:00 p.m., and for HNO3 at all times, the range is small and close tothe actual partial pressure and is not shown.

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Figure 14. The fraction of total particulate A1-5 and B1-5 present in the aqueous phase of the aerosol, over the diurnal cycle. (a) UCD-CACM model result: open circle and solid line – A5; dot and dashed line – A1-4. (b) AIM result: dot and solid line – A1; diamond and solid line – A2 and A4; plus and dashed line – A3; open circle and dashed line – A5. (c) UCD-CACM model result: dot and solid line – B1; open square and dashed line – B2; plus and dashed line – B3 and B4; open circle and solid line B5. (d) AIM result: lines and symbols same as in (c).

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Fig. 14. The fraction of total particulate A1-5 and B1-5 present in the aqueous phase of theaerosol, over the diurnal cycle. (a) UCD-CACM model result: open circle and solid line – A5;dot and dashed line – A1-4. (b) AIM result: dot and solid line – A1; diamond and solid line – A2and A4; plus and dashed line – A3; open circle and dashed line – A5. (c) UCD-CACM modelresult: dot and solid line – B1; open square and dashed line – B2; plus and dashed line – B3and B4; open circle and solid line B5. (d) AIM result: lines and symbols same as in (c).

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Figure 15. The ratios of the amounts of surrogate species B1-5 in the aqueous phase at 8 am, calculated using the UCD-CACM model and AIM (for total aerosol amounts of all species except water fixed to values from the UCD-CACM model). The ratio is equal to AIM / UCD-CACM. Dot and solid line – B1; open circle and dashed line – B2; cross and dash-dot line – B3 and B4; square and dashed line – B5.

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Fig. 15. The ratios of the amounts of surrogate species B1-5 in the aqueous phase at08:00 a.m., calculated using the UCD-CACM model and AIM (for total aerosol amounts ofall species except water fixed to values from the UCD-CACM model). The ratio is equal to AIM/ UCD-CACM. Dot and solid line – B1; open circle and dashed line – B2; cross and dash-dotline – B3 and B4; square and dashed line – B5.

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Figure 16. The fractions of the total aqueous amounts (ntotal) of the water soluble surrogate species A1-5 and B1-2 calculated by AIM to be in the undissociated form (no) at 8 am. A value of no/ntotal of unity corresponds to zero dissociation. Solid circle and dashed line – A1; plus and solid line – A2; open circle and dashed line – A4; dot and dash-dot line – B1; cross and solid line – B2.

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Fig. 16. The fractions of the total aqueous amounts (ntotal) of the water soluble surrogatespecies A1-5 and B1-2 calculated by AIM to be in the undissociated form (no) at 08:00 a.m. Avalue of no/ntotal of unity corresponds to zero dissociation. Solid circle and dashed line – A1;plus and solid line – A2; open circle and dashed line – A4; dot and dash-dot line – B1; crossand solid line – B2.

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Figure 17. Ratios of the equilibrium partial pressures of organic surrogate species for each size bin at 8 am to the actual amounts present in the gas phase in the UCD-CACM model result. (The equilibrium partial pressures were also calculated using the UCD-CACM model.) Values of less than unity correspond to concentrations of the surrogates in the aerosol phase less than those required for equilibrium with the gas phase. Upper plot: surrogates B1-5, as indicated, with the actual vapour pressures of all the surrogates shown in the inset. Lower plot: surrogates A1-5.

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Fig. 17. Ratios of the equilibrium partial pressures of organic surrogate species for each sizebin at 08:00 a.m. to the actual amounts present in the gas phase in the UCD-CACM modelresult. (The equilibrium partial pressures were also calculated using the UCD-CACM model.)Values of less than unity correspond to concentrations of the surrogates in the aerosol phaseless than those required for equilibrium with the gas phase. Upper plot: surrogates B1-5, asindicated, with the actual vapour pressures of all the surrogates shown in the inset. Lower plot:surrogates A1-5. 11040




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62

62

62 Fig. 18.

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Fig. 18. Calculated total amounts (mol m−3) of aerosol phase surrogate organic compoundsover the diurnal cycle. Open squares and open circles with dashed lines – UCD-CACM model;solid symbols and solid lines – AIM calculations. Values for primary compounds P1-8 are thesame for both models. (a) All solids are allowed to form in the AIM calculation, resulting inthe amounts of particulate A1-5 going to negligible values for periods for which the aerosol ispredicted to be dry (contain no water). (b) Only (NH4)2SO4(s) is allowed to form in the AIMcalculation, and the aerosol contains liquid water throughout the cycle. (c) Particulate fractionsof total A1-5, and B1-5. In the AIM calculation all solids are allowed to form, corresponding tothe result in plot (a).

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Figure 19. Calculated fractions of each primary surrogate compound present in the aerosol phase for gas/aerosol equilibrium calculations in which the vapour pressures listed in the first line of Table 5 of Paper II are assigned. More than 99% of P2 and P6 are predicted to occur in the vapour phase (not shown), P8 is assigned entirely to the aerosol phase, as noted in the text, and there is no P5 present in the system.

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Fig. 19. Calculated fractions of each primary surrogate compound present in the aerosol phasefor gas/aerosol equilibrium calculations in which the vapour pressures listed in the first line ofTable 5 of Paper II are assigned. More than 99% of P2 and P6 are predicted to occur in thevapour phase (not shown), P8 is assigned entirely to the aerosol phase, as noted in the text,and there is no P5 present in the system.

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Figure 20. Total particulate masses of each group of surrogate organic compounds, from the AIM calculation of gas/aerosol equilibrium over the diurnal cycle. Solid symbols and line – A and B surrogate compounds in the standard calculation (also shown in Fig. 17b); open symbols and dashed lines – calculation in which the ten surrogate species A1-5 and B1-5 are assumed to obey Raoult’s law “(R)”.

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Fig. 20. Total particulate masses of each group of surrogate organic compounds, from the AIMcalculation of gas/aerosol equilibrium over the diurnal cycle. Solid symbols and line – A and Bsurrogate compounds in the standard calculation (also shown in Fig. 17b); open symbols anddashed lines – calculation in which the ten surrogate species A1-5 and B1-5 are assumed toobey Raoult’s law “(R)”.

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Figure 21. Predicted 24 hr average concentration of SOA on 9 September 1993. (a) Using vapour pressures calculated using boiling points listed in Table 3 of Paper II for the 10 semi-volatile organic species (UCD-CACM method); (b) the increase in SOA concentration obtained when using the same boiling points increased by the uncertainties determined by the ACD boiling point prediction software and listed on the bottom row of Table 3 of Paper II.

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Fig. 21. Predicted 24 h average concentration of SOA on 9 September 1993. (a) Using vapourpressures calculated using boiling points listed in Table 3 of Paper II for the 10 semi-volatileorganic species (UCD-CACM method); (b) the increase in SOA concentration obtained whenusing the same boiling points increased by the uncertainties determined by the ACD boilingpoint prediction software and listed on the bottom row of Table 3 of Paper II.

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Figure 22. The revised structure of surrogate compound B5.

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Fig. 22. The revised structure of surrogate compound B5.

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Figure 23. The reciprocal γNH4

+ /γH+ in pure aqueous (NH4)2SO4 at 298.15 K. Dots – derived from the measurements of Maeda and Iwata (1997); dotted line – calculated using the molality based model of Pitzer (1992); solid line – AIM; dashed line – method of Kusik and Meissner (1978) as used in the UCD-CACM model.

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Fig. 23. The reciprocal γNH+4 /γH+ in pure aqueous (NH4)2SO4 of molality m at 298.15 K. Dots

– derived from the measurements of Maeda and Iwata (1997); dotted line – calculated usingthe molality based model of Pitzer (1992); solid line – AIM; dashed line – method of Kusik andMeissner (1978) as used in the UCD-CACM model.

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